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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.) R. Benedetti and J.-J. Risler, \textit{Real Algebraic and Semi-algebraic Sets}, Actualités Mathématiques, Hermann, Paris, 1990. Real algebraic and real-analytic geometry, Relevant commutative algebra, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic 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.) Kucharz, W., Continuous rational maps into the unit \(2\)-sphere, Arch. Math. (Basel), 102, 257-261, (2014) 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.) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebra, Real algebraic and real-analytic geometry, Finite-dimensional division 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.) Jun, Jaiung: Valuations of semirings. (2015) 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.) Zeng, G.: Computation of generalized real radicals of polynomial ideals, Sci. China ser. A 42, No. 3, 272-280 (1999) Real algebra, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), 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.) Bernd Bank, Marc Giusti, Joos Heintz & Guy Merlin Mbakop, ``Polar varieties and efficient real elimination'', Math. Z.238 (2001) no. 1, p. 115-144 Real algebraic sets, Computational aspects in algebraic geometry, 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.) Favre (C.) and Jonsson (M.).- The valuative tree. Springer (2004). Zbl1064.14024 MR2097722 Singularities of curves, local rings, Trees, Valuations and their generalizations for commutative rings, Integral closure of commutative rings and ideals, Formal power series 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.) Seppälä, M.: Computation of period matrices of real algebraic curves. Discrete comput. Geom. 11, No. 1, 65-81 (1994) Computational aspects of algebraic curves, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Special algebraic curves and curves of low genus, Symbolic computation and algebraic computation, 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, Real polynomials: analytic properties, etc., Semi-analytic sets, subanalytic sets, and generalizations
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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.) 11. Matsumoto, R., Miura, S.: Finding a basis of a linear system with pairwise distinct discrete valuations on an algebraic curve. J. Symb. Comput. 30 (3), 309-323 (2000). Computational aspects of algebraic curves, Geometric methods (including applications of algebraic geometry) applied to coding theory, Valuations and their generalizations for commutative rings, Divisors, linear systems, invertible sheaves, Riemann surfaces; Weierstrass points; gap sequences
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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
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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.) Robson R., Nash wings and real prime divisors Real algebraic and real-analytic geometry, Real-analytic and Nash manifolds, 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.) Sekiguchi, K.: Prüfer domain and affine scheme, Tokyo J. Math. 13, No. 2, 259-275 (1990) Relevant commutative algebra, Dedekind, Prüfer, Krull and Mori rings and their generalizations, 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.) A. Parusiński, Topology of injective endomorphisms of real algebraic sets, Math. Ann. 328 (2004), 353-372. Topology of real algebraic varieties, Real algebraic sets, Germs of analytic sets, local parametrization
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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.) Software, source code, etc. for problems pertaining to algebraic geometry, 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.) Real algebraic sets, General convexity, Syzygies, resolutions, complexes and 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.) Boucksom, S.; Küronya, A.; Maclean, C.; Szemberg, T., Vanishing sequences and Okounkov bodies, Math. Ann., 361, 811-834, (2015) Special divisors on curves (gonality, Brill-Noether theory), Divisors, linear systems, invertible sheaves, Miscellaneous topics in measure theory, 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.) S. Finashin and V. Kharlamov, ''Deformation classes of real four-dimensional cubic hypersurfaces,'' J. Algebraic Geom. 17(4), 677--707 (2008). 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.) K. Kaspers, L. Mathelin, and H. Abou-Kandil, \textit{A machine learning approach for constrained sensor placement}, in Proceedings of the American Control Conference, 2015, pp. 4479--4484, http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=7172034. Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semialgebraic sets and related spaces, Model-theoretic algebra, Model theory of ordered structures; o-minimality
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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.) Michael Temkin, ``On local properties of non-Archimedean analytic spaces. II'', Isr. J. Math.140 (2004), p. 1-27 Non-Archimedean analysis, Rigid analytic geometry, General valuation theory for fields, 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.) Singularities in algebraic geometry, Valuations and their generalizations for commutative rings, Local structure of morphisms in algebraic geometry: étale, flat, 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.) Pedersen, P., Roy, M.-F., Szpirglas, A.: Counting real zeros in the multivariate case. In: Computational algebraic geometry, of Progress in Mathematics. vol. 109, pp. 203-224, Birkhäuser, Boston, (1993) Real algebraic sets, Polynomials in real and complex fields: location of zeros (algebraic theorems), Analysis of algorithms and problem complexity
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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.) Sendra, J.; Winkler, F.: Real parametrization of algebraic curves, artificial intelligence and symbolic computation. (1998) Computational aspects of algebraic curves, Arithmetic ground fields for curves, Symbolic computation and algebraic computation, 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.) Toric varieties, Newton polyhedra, Okounkov bodies, Groups acting on specific manifolds, \(n\)-dimensional polytopes, Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes, Real algebraic sets, Compact groups of homeomorphisms
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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
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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.) Matrix completion problems, Graphs and linear algebra (matrices, eigenvalues, 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.) Families, moduli of curves (algebraic), Real algebraic sets, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Automorphisms of 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.) Polynomials, factorization in commutative rings, Real algebraic sets, Computational aspects of algebraic curves, 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.) M. S. el Din and E. Schost: A baby steps/giant steps probabilistic algorithm for computing roadmaps in smooth bounded real hypersurface, \textit{Discret. Comput. Geom}. \textbf{45}(1), pages 181-220, 2011. Semialgebraic sets and related spaces, Computational aspects in algebraic 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.) McEnerney, J.; Stengle, G., Alternate evidence for nonnegativity, J. pure appl. algebra, 208, 3, (2007) Real algebraic sets, Semialgebraic sets and related spaces
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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.), Germs of analytic sets, local parametrization, Group actions on varieties or schemes (quotients), Semi-analytic sets, subanalytic sets, and generalizations, Real algebraic and real-analytic geometry, Real-analytic manifolds, real-analytic spaces
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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.) Alvis, D.; Johnston, B.; Madden, J.: Complete ideals defined by sign conditions and the real spectrum of two-dimensional local ring. Math. nachr. 174, 21-34 (1995) Regular local rings, Real algebraic sets, Relevant commutative algebra, Actions of groups on commutative rings; invariant theory
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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.) Sujatha, R, Witt groups of real projective surfaces, Math. Ann., 288, 89-101, (1990) Real algebraic sets, Étale and other Grothendieck topologies and (co)homologies, Quadratic forms over global rings and fields, Topological properties in algebraic 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.) 10.2140/pjm.1992.153.31 Real-analytic and Nash manifolds, 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.) Burési, J.: Local-global principle for étale cohomology,K-Theory 9 (1995), 551-566. Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Real algebraic sets, Local rings and semilocal 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.) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Real algebraic sets, Enumerative problems (combinatorial problems) in algebraic 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.) Semidefinite programming, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Moment problems, Nonconvex programming, global optimization, Real algebra, Semialgebraic sets and related spaces
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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.) General valuation theory for fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Field arithmetic, Valued fields, 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.) Bosio, Frédéric; Meersseman, Laurent, Real quadrics in \(\mathbf{C}^n\), complex manifolds and convex polytopes, Acta Math., 197, 1, 53-127, (2006) Real algebraic sets, Real submanifolds in complex 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.) Multiplicity theory and related topics, Valuations and their generalizations for commutative rings, Intersection theory, characteristic classes, intersection multiplicities in algebraic 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.) Batkhin, A-B; Bruno, A-D, Investigation of a real algebraic surface, Program Comput Softw, 41, 74-83, (2015) Real algebraic sets, Computational aspects of algebraic surfaces, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Surfaces in Euclidean and related spaces, 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.) Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation, 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.) Adamaszek, M.; Kozlowski, A.; Yamaguchi, K., Spaces of algebraic and continuous maps between real algebraic varieties, Q. J. Math., 62, 771-790, (2011) 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. COSTE , Sous-ensembles algébriques réels de codimension 2 , (Real Analytic and Algebraic Geometry, Lecture Notes in Math., Springer-Verlag, 1990 , Vol. 1420, pp. 111-120). MR 91c:14069 | Zbl 0723.14040 Real algebraic sets, Linkage
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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} (Springer, Berlin, 1989), Elements of Mathematics. Research exposition (monographs, survey articles) pertaining to commutative algebra, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra, Theory of modules and ideals in commutative rings, 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.) Coste M.: Épaississement d'une hypersurface algébrique réelle. Proc. Jpn. Acad. Ser. A. Math. Sci. 68(7), 175--180 (1992) Real algebraic sets, Hypersurfaces and algebraic 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.) Valuations and their generalizations for commutative rings, Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Singularities of surfaces or higher-dimensional 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.) Scheiderer, C.,Stability index of real varieties. Invent. Math.97 (1989), 467--483. Semialgebraic sets and related spaces, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), 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.) Jacobians, Prym varieties, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Rational points, 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.) K. Kurdyka and A. Parusiński, Arc-symmetric sets and arc-analytic mappings, Arc spaces and additive invariants in real algebraic and analytic geometry, Panor. Synthèses 24, Société Mathématique de France, Paris (2007), 33-67. Real algebraic sets, Topology of real algebraic varieties, Germs of analytic sets, local parametrization, Real-analytic manifolds, real-analytic spaces, Real-analytic and Nash 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.) Real algebraic sets, Singularities of surfaces or higher-dimensional varieties, Computational aspects of algebraic surfaces, Real-analytic manifolds, real-analytic spaces
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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, and, O. Viro, Maximal real algebraic hypersurfaces of projective space, in preparation. Real algebraic sets, Transcendental methods, Hodge theory (algebro-geometric aspects), Hypersurfaces and algebraic 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.) Vinberg, E.B.: Some arithmetical discrete groups in Lobacevskii spaces, In: \textit{Discrete Subgroups of Lie Groups and Applications to Moduli}, Oxford, 1975, pp. 328-348 Real algebraic sets, Families, moduli, classification: algebraic theory
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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.) Dovermann, K. H.; Masuda, M.; Suh, D. Y.: Nonisomorphic algebraic models of a smooth manifold with group action. Proc. amer. Math. soc. 123, 55-61 (1995) Real algebraic sets, Group actions on varieties or schemes (quotients), 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.) Real algebraic sets, Topological rings and modules
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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.) Kiyek, K.; Vicente, J. L., Resolution of curve and surface singularities in characteristic zero, (2004), Kluwer Dordrecht Research exposition (monographs, survey articles) pertaining to algebraic geometry, Valuations and their generalizations for commutative rings, Singularities in algebraic geometry, Singularities of curves, local rings, Singularities of surfaces or higher-dimensional varieties, Analytic algebras and generalizations, preparation theorems, Sheaves of differential operators and their modules, \(D\)-modules, 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.) Pseudoholomorphic curves, Topology of real algebraic varieties, 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.) Commutative semigroups, Singularities of curves, local rings, Valuations and their generalizations for commutative rings, Software, source code, etc. for problems pertaining to group theory
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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 and real-analytic 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.) Polynomial optimization, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Semialgebraic sets and related spaces, Computational real algebraic geometry, Semidefinite programming
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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.) Bodin, A.: Non-reality and non-connectivity of complex polynomials. C. R. Math. acad. Sci. Paris 335, 1039-1042 (2002) Topology of real algebraic 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.) G. Fichou, J. Huisman, F. Mangolte and J.-P. Monnier, Fonctions régulues, J. reine angew. Math. (2015), 10.1515/crelle-2014-0034. Real algebraic sets, Nash functions and manifolds, Rational and birational maps, Vanishing theorems in algebraic geometry, 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.) S. Kuhlmann and M. Putinar, \textit{Positive polynomials on fibre products}, C. R. Math. Acad. Sci. Paris, 344 (2007), pp. 681--684. Real algebra, 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, Toric varieties, Newton polyhedra, Okounkov bodies, Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Computational real algebraic 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.) P. Philippon : Critères pour l'indépendance algébrique dans les anneaux diophantiens , C.R. Acad. Sci. Paris Sér. I 315 (1992) 511-515. Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial), Relevant commutative algebra, 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.) Kurdyka, K.; Spodzieja, S., Separation of real algebraic sets and the łojasiewicz exponent, Proc. Am. Math. Soc., 142, 3089-3102, (2014) Real-analytic sets, complex Nash functions, Real algebraic sets, Local complex singularities, Dynamics induced by flows and semiflows
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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. M. Bhatwadekar and Raja Sridharan, Zero cycles and Euler class groups of smooth real affine varieties, Invent. Math., 136 (1999), 287--322. Algebraic cycles, Projective and free modules and ideals in commutative 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.) Dickmann, M.; Gluschankof, D.; Lucas, F., The order structure of the real spectrum of commutative rings, J. Algebra, 229, 175-204, (2000) Ordered rings, Real algebraic sets, Ordered rings, algebras, modules
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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.) Mustaţă, M.; Nicaise, J., Weight functions on non-Archimedean analytic spaces and the Kontsevich-Soibelman skeleton, Algebr. Geom., 2, 3, 365-404, (2015) Rigid analytic geometry, Valuations and their generalizations for commutative rings, Vanishing theorems in algebraic 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.) Ordered fields, Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Ordered 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.) Cutkosky, S. D.; Dalili, Kia; Kashcheyeva, Olga: Growth of rank 1 valuation semigroups. Commun. algebra 38, 2768-2789 (2010) Valuations and their generalizations for commutative rings, Global theory and resolution of singularities (algebro-geometric aspects), Ordered semigroups and monoids
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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, Real algebraic sets, Real-analytic and Nash 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.) Real algebraic sets, Semialgebraic sets and related spaces
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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.) Itenberg, I., Kharlamov, V., and Shustin, E.: Welschinger invariant and enumeration of real rational curves. \textit{International Math. Research Notices }49 (2003), 2639--2653. Real algebraic sets, Enumerative problems (combinatorial problems) in algebraic 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.) Valuations and their generalizations for commutative rings, Local rings and semilocal rings, Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Singularities of surfaces or higher-dimensional 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.) Valuations and their generalizations for commutative rings, Singularities of curves, local rings, 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.) 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.) Fernando, On the spectra of rings of semialgebraic functions, Collect. Math. 63 (3) pp 299-- (2012) Semialgebraic sets and related spaces, Extension of maps, Real-valued functions in general topology, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Chain conditions, finiteness conditions in commutative ring theory
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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, Coverings of curves, fundamental group, Real algebraic sets, Dessins d'enfants theory, Exact enumeration problems, generating functions, Enumeration in graph theory
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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.) Acevedo, José; Velasco, Mauricio, Test sets for nonnegativity of polynomials invariant under a finite reflection group, J. Pure Appl. Algebra, 220, 8, 2936-2947, (2016) Reflection and Coxeter groups (group-theoretic aspects), 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.) Becker, Eberhard: Sums of squares and quadratic forms in real algebraic geometry, Cahiers sém. Hist. math. Sér. 2 1, 41-57 (1991) Real algebraic sets, Quadratic forms over general 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.) Kamiyama Y. and Tezuka M. (1999). Topology and geometry of equilateral polygon linkages in the Euclidean plane. Q. J. Math. 50: 463--470 General low-dimensional topology, Discriminantal varieties and configuration spaces in algebraic 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.) Real algebraic and real-analytic geometry, 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.) Giraud, J.: Étude locale des singularités. Publications Mathématiques d'Orsay, Number~26. Mathématique, Université Paris XI, Orsay, 1972. Cours de 3éme cycle (1971-1972) Valuations and their generalizations for commutative rings, Valued fields, General valuation theory for fields, Singularities 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.) Müller, D., Local solvability of linear differential operators with double characteristics. I. Necessary conditions, Math. Ann, 340, 1, 23-75, (2007) Hypoelliptic equations, Analysis on other specific Lie groups, Nilpotent and solvable Lie 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.) Campillo, A. and Castellanos, J.: ''Arf Closure relative to a divisorial valuation and trasversal curves''. Preprint 1991 Valuations and their generalizations for commutative rings, Integral closure of commutative rings and ideals, Singularities of curves, local rings, Commutative Noetherian rings and modules, 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.) M. Coste, T. Fukui, K. Kurdyka, C. McCrory, A. Parusiński and L. Paunescu, Arc spaces and additive invariants in Real Algebraic and Analytic Geometry. Panoramas et Synthèses 24, Soc. Math. France (2007). Real algebraic and real-analytic geometry, Real algebraic sets, Semialgebraic sets and related spaces, Topology of real algebraic varieties, Semi-analytic sets, subanalytic sets, and generalizations
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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.) Andradas, C.: Real places in function fields. Ph.d. dissertation (1983) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Real algebraic and real-analytic geometry, Valued 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.) Conrad, B., Deligne\(###\)s notes on Nagata compactification, J. Ramanujan Math. Soc., 22, 205-257, (2007) Schemes and morphisms, Birational geometry, Embeddings in algebraic geometry, Rational and birational maps, 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.) Erdős problems and related topics of discrete geometry, Real algebraic sets, Convex sets in \(n\) dimensions (including convex hypersurfaces), Arrangements of points, flats, hyperplanes (aspects of discrete 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.) [14] Michel Vaquié, &Extensions de valuation et polygone de Newton
nn. Inst. Fourier (Grenoble)58 (2008) no. 7, p.~2503-Cedram | &MR~24 | &Zbl~1170. Valuations and their generalizations for commutative rings, Valued fields, 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.) J. Bochnak and W. Kucharz, \?-theory of real algebraic surfaces and threefolds, Math. Proc. Cambridge Philos. Soc. 106 (1989), no. 3, 471 -- 480. Applications of methods of algebraic \(K\)-theory in algebraic geometry, Real algebraic sets, \(3\)-folds, Grothendieck groups and \(K_0\)
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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 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.) Georges Comte & Chris Miller, ``Points of bounded height on oscillatory sets'', to appear in \(Q. J. Math.\), , 2017 Real-analytic manifolds, real-analytic 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.) Real algebraic and real-analytic geometry, Birational geometry, Generalizations (algebraic spaces, stacks), 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.) Klep, I.; Vinnikov, V.; Volčič, J., Null- and positivstellensätze for rationally resolvable ideals Noncommutative algebraic geometry, Real algebra, Other kinds of identities (generalized polynomial, rational, involution), Other ``noncommutative'' mathematics based on \(C^*\)-algebra 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.) Sinn, R., Algebraic boundaries of \(S O(2)\)-orbitopes, Discrete comput. geom., 50, 219-235, (2013) Real algebraic sets, General convexity, Semidefinite programming, Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.), Computational aspects of algebraic 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.) Orthogonal matrices, Combinatorial aspects of matrices (incidence, Hadamard, 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.) Madden, J.; Schwartz, N.: Separating ideals in dimension 2. Rev. mat. Univ. comp. Madrid 10, 217-240 (1997) Real algebra, Semialgebraic sets and related spaces, Valuations and their generalizations for commutative rings, Singularities of curves, local rings
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