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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) De La Puente, M. J.: The compatible valuation rings of the coordinate ring of the real plane. Contemp. math. 155 (1994) Real algebraic sets, Valuation rings, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Machura, M., Osiak, K.: Spaces of \({\mathbb{R}}\) -places of rational function fields. arXiv:0803.0676 (2008) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields, Valued fields, Valuations and their generalizations for commutative rings, Real algebraic and real-analytic geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Crespo, Teresa; Hajto, Zbigniew, Real Liouville extensions, Comm. Algebra, 0092-7872, 43, 5, 2089-2093, (2015) Differential algebra, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic sets, Galois theory and commutative ring extensions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Differential algebra, Galois theory and commutative ring extensions, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Differential algebra, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Lasserre J.B. (2005). SOS approximations of polynomials nonnegative on a real algebraic set. SIAM J. Optim. 16: 610--208 Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semidefinite programming, Convex programming, Sums of squares and representations by other particular quadratic forms
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Colliot-Thélène, J.-L., \textit{the Noether-Lefschetz theorem and sums of 4 squares in the rational function field \textbf{R}(\textit{x}, \textit{y})}, Compos. Math., 86, 235-243, (1993) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Algebraic theory of quadratic forms; Witt groups and rings, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Antonio Campillo and Jesús M. Ruiz, Some remarks on Pythagorean real curve germs, J. Algebra 128 (1990), no. 2, 271 -- 275. Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Henselian rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic sets, Real polynomials: location of zeros, Forms over real fields, Sums of squares and representations by other particular quadratic forms, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Convex programming, Algebraic combinatorics
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Schülting, H. W.: The binary class group of the real holomorphy ring. (1986) Valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Forms over real fields, Real algebraic and real-analytic geometry, Valuations and their generalizations for commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Varieties and morphisms, Ordered fields, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) M. Putinar and C. Scheiderer, \textit{Hermitian algebra on the ellipse}, Illinois J. Math., 56 (2012), pp. 213--220. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic sets, Hermitian, skew-Hermitian, and related matrices, CR manifolds as boundaries of domains
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Rational points, Linear algebraic groups over arbitrary fields, Other nonalgebraically closed ground fields in algebraic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Topology of real algebraic varieties, Normed fields
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Nonlinear programming, Convex sets in \(n\) dimensions (including convex hypersurfaces), Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Polynomial optimization, Computational real algebraic geometry, Numerical methods involving duality, Semidefinite programming, Nonconvex programming, global optimization, Nonlinear programming, Real algebraic sets, Convex programming, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Rational points, Linear algebraic groups over arbitrary fields, Other nonalgebraically closed ground fields in algebraic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Lombardi, H.: Théorème effectif des zéros réel et variantes. Publications mathématiques de besançon 1 (1988--1989) Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Effectivity, complexity and computational aspects of algebraic geometry, Relevant commutative algebra
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) SCHÜLTING, H.W.: Prime divisors on real varieties and valuation theory. J. Alg.98, 499-514 (1986) Valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Forms over real fields, Real algebraic and real-analytic geometry, Valuations and their generalizations for commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) DOI: 10.1090/S0002-9939-2011-10841-4 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic sets, Hermitian, skew-Hermitian, and related matrices, CR manifolds as boundaries of domains
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic sets, Real polynomials: analytic properties, etc.
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semidefinite programming, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) G. Blekherman, \textit{There are significantly more nonnegative polynomials than sums of squares}, Israel J. Math., 153 (2006), pp. 355--380. Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Mixed volumes and related topics in convex geometry, Inequalities and extremum problems involving convexity in convex geometry, Integral geometry
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) E. Becker, R. Berr, F. Delon, D. Gondard, Hilbert's 17-th problem for sums of 2n-th powers, preprint Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Forms of degree higher than two, Valued fields, Ordered fields
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Semialgebraic sets and related spaces, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered fields
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Semialgebraic sets and related spaces, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Special algebraic curves and curves of low genus
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ideals and multiplicative ideal theory in commutative rings, Valuations and their generalizations for commutative rings, Extension theory of commutative rings, Integral closure of commutative rings and ideals, Valuation rings, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Topology of real algebraic varieties, Deformations of singularities, Local deformation theory, Artin approximation, etc., Singularities of curves, local rings, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Valuations and their generalizations for commutative rings, Semigroup rings, multiplicative semigroups of rings, Arithmetic ground fields for curves
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ramification problems in algebraic geometry, Valuations and their generalizations for commutative rings, Rings of fractions and localization for commutative rings, Arithmetic rings and other special commutative rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Determinantal varieties, Vector spaces, linear dependence, rank, lineability, Determinants, permanents, traces, other special matrix functions, Eigenvalues, singular values, and eigenvectors, Minimal surfaces and optimization, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Friedland, SIAM Journal on Matrix Analysis and Applications 13 pp 1142-- (1992) Eigenvalues, singular values, and eigenvectors, Hermitian, skew-Hermitian, and related matrices, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Implicit function theorems, Jacobians, transformations with several variables, Real polynomials: analytic properties, etc., Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Jacobian problem
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) S. Fiedler-Le Touzé and S. Yu. Orevkov, A flexible affine \?-sextic which is algebraically unrealizable, J. Algebraic Geom. 11 (2002), no. 2, 293 -- 310. Real algebraic sets, Plane and space curves
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Extension theory of commutative rings, Rings of fractions and localization for commutative rings, Integral domains, Valuations and their generalizations for commutative rings, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Plane and space curves
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Permutations, words, matrices, Exact enumeration problems, generating functions, Other combinatorial number theory, Special aspects of infinite or finite groups, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) --------, Welschinger invariants of small non-toric del Pezzo surfaces, J. Europ. Math. Soc. 15 (2013), 539--594. Enumerative problems (combinatorial problems) in algebraic geometry, Real algebraic sets, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Campesato, JB, An inverse mapping theorem for blow-Nash maps on singular spaces, Nagoya Math. J., 223, 162-194, (2016) Semialgebraic sets and related spaces, Singularities in algebraic geometry, Arcs and motivic integration, Real algebraic sets, Nash functions and manifolds
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Basarab, Serban A.: Definite functions on algebraic varieties over ordered fields. Rev. roumaine math. Pures appl. 29, 527-535 (1984) Ordered fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Rational points, Real algebraic and real-analytic geometry, Model-theoretic algebra, Foundations of classical theories (including reverse mathematics)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) B. Bank, M. Giusti, J. Heintz, L. Lehmann, and L. M. Pardo, \textit{Algorithms of intrinsic complexity for point searching in compact real singular hypersurfaces}, Found. Comput. Math. \textbf{12} (2012), no. 1, 75-122. Real algebraic sets, Singularities in algebraic geometry, Deformations of singularities, Symbolic computation and algebraic computation
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Computational aspects of algebraic curves, Computational aspects of algebraic surfaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) I. Itenberg, Groups of monodromy of non-singular curves of degree 6, Real Analytic and Algebraic Geometry, Proceedings, Trento (Italy) 1992, Walter de Gruyter, (1995), 161--168. Special algebraic curves and curves of low genus, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Computational aspects of higher-dimensional varieties, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Kourganoff, M.: Universality theorems for linkages in homogeneous surfaces (2014, preprint). arXiv:1407.6815 Elementary problems in hyperbolic and elliptic geometries, Real algebraic sets, Semialgebraic sets and related spaces, Local differential geometry of Lorentz metrics, indefinite metrics, Discriminantal varieties and configuration spaces in algebraic topology
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Algebraic cycles, Rational and birational maps, Realizing cycles by submanifolds, Toric varieties, Newton polyhedra, Okounkov bodies
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) J. Colliot-Thélène, ''Principe local-global pour les zéro-cycles sur les surfaces réglées,'' J. Amer. Math. Soc., vol. 13, iss. 1, pp. 101-127, 2000. (Equivariant) Chow groups and rings; motives, Brauer groups of schemes, Algebraic cycles, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Arithmetic ground fields for surfaces or higher-dimensional varieties, Global ground fields in algebraic geometry, Varieties over global fields, Rational and ruled surfaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Kucharz W.: Cycles on algebraic models of smooth manifolds. J. Eur. Math. Soc. (JEMS) 11, 393--405 (2009) Real algebraic sets, Topology of real algebraic varieties, Algebraic topology on manifolds and differential topology
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Campillo, A., Delgado, F., Gusein-Zade, S.: On Poincaré series of filtrations on equivariant functions of two variables. Mosc. Math. J. 7(2), 243-255 (2007) Singularities in algebraic geometry, Filtered associative rings; filtrational and graded techniques, Actions of groups and semigroups; invariant theory (associative rings and algebras), Valuations and their generalizations for commutative rings, Singularities of curves, local rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Fekak ( A. ) .- Interpretation algébrique de l'exposant de Łojasiewicz , Annales Polonici Mathematici, LVI, 2, 123 - 131 ( 1992 ). MR 1159983 | Zbl 0773.14027 Semialgebraic sets and related spaces, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Valette, Guillaume, Multiplicity mod 2 as a metric invariant, Discrete Comput. Geom., 43, 663-679, (2010) Real algebraic sets, Multiplicity theory and related topics, Complex singularities
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) S. Ishii, ''Arcs, valuations and the Nash map,'' J. Reine Angew. Math., vol. 588, pp. 71-92, 2005. Singularities in algebraic geometry, Valuations and their generalizations for commutative rings, Toric varieties, Newton polyhedra, Okounkov bodies, Divisors, linear systems, invertible sheaves
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Positive matrices and their generalizations; cones of matrices, Real algebraic sets, Convex sets and cones of operators
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) G. Mikhalkin, \textit{Real algebraic curves, the moment map and amoebas}, Ann. Math. 151 (2000), 309--326. Real algebraic sets, Topology of real algebraic varieties, Configurations and arrangements of linear subspaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Rational points, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) V. F. Ignatenko, ''On an infinite group of skew symmetries,''Izv. Vuzov. Mat., No. 3, 32--34 (1994). Analytic and descriptive geometry, Real algebraic and real-analytic geometry, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [2] Frédéric Campana &aThomas Peternell, &Algebraicity of the ample cone of projective varieties&#xJ. Reine Angew. Math.407 (1990), p.~160-MR~10 | &Zbl~0728. Divisors, linear systems, invertible sheaves, Real algebraic sets, Picard groups
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Enumerative problems (combinatorial problems) in algebraic geometry, Real algebraic sets, Rational and ruled surfaces, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
| 0
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Valuations and their generalizations for commutative rings, Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Semigroup rings, multiplicative semigroups of rings
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ballico, E; Ghiloni, R, The principle of moduli flexibility for real algebraic manifolds, Ann. Polon. Math., 109, 1-28, (2013) Nash functions and manifolds, Real algebraic sets, Topology of real algebraic varieties
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Dumnicki, Marcin; Harbourne, Brian; Küronya, Alex; Roé, Joaquim; Szemberg, Tomasz, Very general monomial valuations of \(\mathbb{P}^2\) and a Nagata type conjecture, Comm. Anal. Geom., 25, 1, 125-161, (2017) Divisors, linear systems, invertible sheaves, Valuations and their generalizations for commutative rings, Rational and ruled surfaces
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Symbolic computation and algebraic computation, Real algebraic sets, Computer graphics; computational geometry (digital and algorithmic aspects)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Lefèvre-Hasegawa, K.: Sur les \(A_\infty \)-catégories, Ph.D. thesis. Université Paris 7--Denis Diderot, (2003) Topological quantum field theories (aspects of differential topology), Topological field theories in quantum mechanics, Noncommutative geometry methods in quantum field theory, Relationships between algebraic curves and physics, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ruiz, J.: Central orderings in fields of real meromorphic function germs. Preprint (1984) Real algebraic and real-analytic geometry, Real-analytic manifolds, real-analytic spaces, Germs of analytic sets, local parametrization, Real-analytic functions, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) A. F. Costa and M. Izquierdo, On the locus of real algebraic curves, Atti Sem. Mat. Fis. Univ. Modena 49 (2001), no. suppl., 91 -- 107. Dedicated to the memory of Professor M. Pezzana (Italian). Real algebraic sets, Families, moduli of curves (algebraic), Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), Compact Riemann surfaces and uniformization
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Semialgebraic sets and related spaces, Real rational functions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Bonnard, I., Description of algebraically constructible functions, Adv. Geom., 3, 145-161, (2003) Real algebraic sets, Topology of real algebraic varieties
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Varieties and morphisms, Real algebraic sets, Real algebraic and real-analytic geometry, Topology of vector bundles and fiber bundles
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Picard groups, Special algebraic curves and curves of low genus
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ballico, E.: Gonality and Clifford index for real algebraic curves, Collectanea math. 53 (2002) Special divisors on curves (gonality, Brill-Noether theory), Real algebraic sets, Plane and space curves
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Ernström, Lars, Topological Radon transforms and the local Euler obstruction, Duke Math. J., 0012-7094, 76, 1, 1-21, (1994) Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants, Global theory of complex singularities; cohomological properties, Real algebraic sets, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Molecular structure (graph-theoretic methods, methods of differential topology, etc.), Genetics and epigenetics, Semidefinite programming, Rigidity and flexibility of structures (aspects of discrete geometry), Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Kucharz, W., Regular versus continuous rational maps, Topol. Appl., 160, 1375-1378, (2013) Real algebraic sets, Topology of real algebraic varieties
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Semialgebraic sets and related spaces, Real algebraic sets, Vector and tensor algebra, theory of invariants, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Nash functions and manifolds, Absolute neighborhood retracts, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) N. Bourbaki, \textit{Commutative Algebra}, Chapters 1-7, Elements of Mathematics (Berlin) (Springer-Verlag, Berlin, 1998); Translated from the French; Reprint of the 1989 English translation. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra, Theory of modules and ideals in commutative rings, Research exposition (monographs, survey articles) pertaining to commutative algebra, Collected or selected works; reprintings or translations of classics, Topological rings and modules, Ideals and multiplicative ideal theory in commutative rings, Valuations and their generalizations for commutative rings, Divisors, linear systems, invertible sheaves
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Gondard-Cozette, D.: Chainable fields and real algebraic geometry. Lecture notes in math. 1420 (1990) Ordered fields, Real algebraic sets, Real and complex fields
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Bochnak, J.; Kucharz, W.: On polynomial mappings into spheres. Ann. polon. Math. 51, 89-97 (1990) Topology of real algebraic varieties, Polynomials over commutative rings, Real-valued functions in general topology, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Jacobians, Prym varieties, Special divisors on curves (gonality, Brill-Noether theory), Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Algebraic cycles
| 0
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) A. Conca, D. Edidin, M. Hering, and C. Vinzant, \textit{An algebraic characterization of injectivity in phase retrieval}, Appl. Comput. Harmon. Anal., 38 (2015), pp. 346--356. Trigonometric approximation, Signal theory (characterization, reconstruction, filtering, etc.), Information theory (general), Real algebraic sets
| 0
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Multiplicity theory and related topics, Valuations and their generalizations for commutative rings, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
| 0
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Andrei Gabrielov and Askold Khovanskii. Multiplicity of a Noetherian intersection. In: \textit{Geometry of differential equations}, volume 186 of \textit{Amer. Math. Soc. Transl. Ser. 2}, pages 119-130. Amer. Math. Soc., Providence, RI (1998). Semi-analytic sets, subanalytic sets, and generalizations, Real algebraic sets, Local complex singularities
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Monnier, J. -P.: Witt group and torsion Picard group of real curves. J. pure appl. Algebra 169, 267-293 (2002) Picard groups, Topology of real algebraic varieties, Algebraic theory of quadratic forms; Witt groups and rings, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Foundations of tropical geometry and relations with algebra, Non-Archimedean valued fields, Formal power series rings, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Computational aspects of higher-dimensional varieties, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Frédéric Mangolte, Une surface réelle de degré 5 dont l'homologie est entièrement engendrée par des cycles algébriques, C. R. Acad. Sci. Paris Sér. I Math. 318 (1994), no. 4, 343 -- 346 (French, with English and French summaries). Singularities of surfaces or higher-dimensional varieties, Real algebraic sets, Classical real and complex (co)homology in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real algebraic sets, Polynomials in real and complex fields: location of zeros (algebraic theorems), Semialgebraic sets and related spaces, Research exposition (monographs, survey articles) pertaining to algebraic geometry
| 0
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Design techniques (robust design, computer-aided design, etc.), Real algebraic sets, Computational aspects in algebraic geometry, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Bochnak, J.; Kucharz, W., Polynomial mappings from products of algebraic sets into spheres, J. Reine Angew. Math., 417, 135-139, (1991) Real algebraic sets, Rational and birational maps
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) M. Passare and J. J. Risler, \textit{On the curvature of the real amoeba}, Proceedings of the G''okova Geometry-Topology Conference 2010, Int. Press, Somerville, MA, 2011, pp. 129--134. Plane and space curves, Toric varieties, Newton polyhedra, Okounkov bodies, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Banakh T., Potyatynyk O., Dimension of graphoids of rational vector-functions, Topology Appl., 2013, 160(1), 24--44 Unicoherence, multicoherence, Dimension theory in algebraic topology, Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants), Real algebraic sets, Real rational functions, Degree, winding number, Topology of special sets defined by functions
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Delzell, Charles N.; Madden, James J., A completely normal spectral space that is not a real spectrum, J. Algebra, 169, 1, 71-77, (1994) Real algebraic sets, Real and complex fields, Relevant commutative algebra
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Gebauer, R.; Kalkbrener, M.; Wall, B.; Winkler, F., CASA: A computer algebra package for constructive algebraic geometry, (), 403-410 Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Computational aspects of algebraic surfaces, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) S. Finashin, V. Kharlamov, Abundance of real lines on real projective hypersurfaces. Int. Math. Res. Notices 16, 3639--3646 (2013) Real algebraic sets
| 0
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Real polynomials: analytic properties, etc., Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Moment problems
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) E. Brugallé, Floor diagrams relative to a conic, and GW-W invariants of del Pezzo surfaces, Adv. Math. 279 (2015), 438--500. Enumerative problems (combinatorial problems) in algebraic geometry, Real algebraic sets, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Topology of real algebraic varieties
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Configurations and arrangements of linear subspaces, Combinatorial aspects of representation theory, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) DOI: 10.1007/BF01265347 Classical real and complex (co)homology in algebraic geometry, Real algebraic sets, Algebraic cycles
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) External book reviews, Research exposition (monographs, survey articles) pertaining to functions of a complex variable, Research exposition (monographs, survey articles) pertaining to potential theory, Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces, Research exposition (monographs, survey articles) pertaining to partial differential equations, Analytic continuation of functions of one complex variable, Boundary value and inverse problems for harmonic functions in higher dimensions, Power series, series of functions of several complex variables, Analyticity in context of PDEs, Real algebraic sets
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DOI: 10.1016/0021-8693(91)90169-9 Valuations and their generalizations for commutative rings, Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) Stengle, G.; McEnerney, J., A semi-algebraic closure for commutative algebra, J. pure appl. algebra, 215, 2257-2261, (2011) Ideals and multiplicative ideal theory in commutative rings, Real algebraic sets, Semialgebraic sets and related spaces
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