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cc233c23b652fd68207c1eca8d2920a729c53856 | schadt has appeared on cnn, cnbc, bbc, bloomberg | schadt has appeared on cnn, cnbc, bbc, bloomberg radio, and bloomberg tv. he and his scientific projects have been profiled in the new york times, esquire magazine, bloomberg businessweek, among others, and several scientific trade publications. the huffington post published a commentary by schadt, calling on scientist... | wikipedia |
c9607d6f4609bbeac4b7f5b4a9b1bb2fe457922d | schadt founded sema4, "a patient-centered health intelligence company | schadt founded sema4, "a patient-centered health intelligence company dedicated to advancing healthcare through data-driven insights," in june 2017. the company uses centrellis™, their health analytics platform, to build predictive models of human health and generate personalized medicine insights. sema4, which was nam... | wikipedia |
eee198921d4dd975c55bc8b1c34fd461ed189622 | in may 2014, schadt and his team announced | in may 2014, schadt and his team announced the resilience project in collaboration with sage bionetworks. the project intended to perform genotyping on as many as 1 million people to find protective biological mechanisms that prevent disease-causing genetic mutations from becoming active. participants were to be health... | wikipedia |
d689d668c615d11650162915a5774a213264dd8c | schadt's team was cited as the reason the | schadt's team was cited as the reason the icahn school of medicine at mount sinai was named #5 of the top 10 most innovative organizations in big data by fast company in a 2014 ranking. according to the article, "the new york city hospital is bringing on top silicon valley talent to build a facility that will map patie... | wikipedia |
91df5d9a56311982ccdef1cc500dc2de065fef88 | in 2013, schadt and his team were awarded | in 2013, schadt and his team were awarded a grant from the national institutes of health to study biological networks in alzheimer's disease. they also published a paper in cell reporting that a network of genes linked to inflammatory response plays a role in late-onset alzheimer's disease. also that year, schadt joine... | wikipedia |
d3f6e655a22c0cb31162bdbfa10f25e0b5cc5d90 | in 2011, schadt joined the mount sinai school | in 2011, schadt joined the mount sinai school of medicine in new york, where he founded the new icahn institute for genomics and multiscale biology and became chair of the department of genetics and genomics sciences. the new institute was launched with $100 million for the first five years and is co-directed by andrew... | wikipedia |
7560fa071f5c56aca72588106a338786e6468e96 | also in 2009, schadt joined dna sequencing company | also in 2009, schadt joined dna sequencing company pacific biosciences as the chief scientific officer. during his time there, schadt demonstrated the application of smrt sequencing technology for various applications, including to sequence bacterial genomes of public health concern to provide real-time information abo... | wikipedia |
9c8cc4200bc35687d84b37fc2d179bc067ef178c | in 2009, along with stephen friend, schadt founded | in 2009, along with stephen friend, schadt founded sage bionetworks, a nonprofit organization with the goal of encouraging collaboration between academic and commercial scientists in performing network-based studies of disease and making the data publicly available. when merck closed down the rosetta business unit, it ... | wikipedia |
5f35fb5261765b8f68a12d9512750cfe5b00854c | demonstrating the ability to infer causal relationships among | demonstrating the ability to infer causal relationships among features in high dimensional data using dna variation information, schadt and his colleagues at merck began reconstructing predictive networks that were shown to be causally associated with disease, leading to the idea of targeting networks, not single genes... | wikipedia |
1dba8815fc1e5cf64e61e732008e6e4ed3842640 | in 1999, after becoming acquainted with stephen friend, | in 1999, after becoming acquainted with stephen friend, he was hired as chief scientist at rosetta inpharmatics, a startup biotech company focused on the generation and analysis of high-dimensional functional genomics data. merck acquired rosetta in 2001, which allowed schadt to combine large-scale molecular profiling ... | wikipedia |
43aafd08b9a74b95b01370614a0c0c72047e4fc9 | while completing his phd, schadt joined roche bioscience | while completing his phd, schadt joined roche bioscience in 1998 as a senior research scientist and began his work on dna microarrays, designing novel algorithms to process and interpret these data. he published some of the first independently developed algorithms to process gene chip data work that he later applied to... | wikipedia |
2df9af347e4d864ac57fad8f7e1fc402a8e0c455 | in 1983, schadt left high school early to | in 1983, schadt left high school early to enlist in the united states air force and joined a special operations/rescue unit. after sustaining a serious shoulder injury that required reconstructive surgery, schadt attended california polytechnic state university on a military scholarship to study computer science and ma... | wikipedia |
c1af3b7570e166e2524a019fd0024002ec97d4bf | schadt's work combines supercomputing and advanced computational modeling | schadt's work combines supercomputing and advanced computational modeling with diverse biological data to understand the relationship between genes, gene products, other molecular features such as cells, organs, organisms, and communities and their impact on complex human traits such as disease. he is known for calling... | wikipedia |
d2a6d47f13d1bc14695dc6e9b0032906bcee66c4 | eric emil schadt (born january 31, 1965) is | eric emil schadt (born january 31, 1965) is an american mathematician and computational biologist. he is founder and former chief executive officer of sema4, a patient-centered health intelligence company, and dean for precision medicine and mount sinai professor in predictive health and computational biology at the ic... | wikipedia |
a6bd5cc9377a9f23d6d8eacda3b4ff6f587545af | embelia schimperi is a shrub or small tree | embelia schimperi is a shrub or small tree that is capable of reaching 6 m (20 ft) in height with a red to brownish bark that is usually smooth. branches are lenticellate and the stems are smooth and free of hair. leaves are oblong to ovate in outline; leaflets can reach up to 12 cm (4.7 in) in length and 5 cm (2.0 in)... | wikipedia |
31a9f277432af049aac9b623063721db5f6822c0 | claire judith horwell is a professor of geohealth | claire judith horwell is a professor of geohealth in the department of earth sciences and institute of hazard, risk and resilience at durham university and the founding director of the international volcanic health hazard network (ivhhn). she studies the health hazards of natural and industrial mineral dusts and commun... | wikipedia |
0e2fae05da657c8168ba0e6820c161ac639e6370 | horwell has published more than 60 papers and | horwell has published more than 60 papers and several book chapters across disciplines including volcanology, petrology, behavioural science, social anthropology, toxicology, exposure science, public health and epidemiology, law and ethics. a full list of publications can be found at: https://www.durham.ac.uk/staff/cla... | wikipedia |
da112b03eda1a73afae1392c99fb24fdafee483c | she created the health interventions in volcanic eruptions | she created the health interventions in volcanic eruptions (hive) consortium project (funded by elrha) to collect evidence on respiratory protection for communities. she investigated the effectiveness of facemasks distributed by agencies during volcanic eruptions, looking to identify whether or not they could adequatel... | wikipedia |
59ee745f408c9c94146b1a27045a465980bfd235 | she has worked with the pan american health | she has worked with the pan american health organization to introduce new epidemiological protocols for use in volcanic crises and has supported many governmental agencies and non-governmental organizations in indonesia, new zealand, singapore, japan, st vincent and mexico in preparing for, and responding to, community... | wikipedia |
29f4ac803d85598a78c2c370f46c6115f5ce11f9 | horwell studies the health hazards of mineral dusts, | horwell studies the health hazards of mineral dusts, and ways to support communities to protect themselves from inhaling particulate air pollution. she uses physicochemical analysis to establish whether or not, and how, mineral particles are harmful, as well as toxicological assessments to determine the respiratory haz... | wikipedia |
8d30ea0f9616285d291fed93dcb4a8ac65435a01 | horwell has served as an advisor to the | horwell has served as an advisor to the world health organization, uk cabinet office and public health england. she was appointed to the government of the united kingdom scientific advisory group for emergencies for volcanic eruptions in 2015. she was president (and, formerly, president-elect) and founding leader of th... | wikipedia |
51362f98478d73d21281472fb34f550dfab82ac2 | in 2003, horwell founded the international volcanic health | in 2003, horwell founded the international volcanic health hazard network through a leverhulme trust network grant. ivhhn provides information on the health hazards and impacts of volcanic emissions to the general public and civil protection agencies, and helps governments prepare for the health response to volcanic er... | wikipedia |
5a43c547f7958d9532c29546c2f896482dd95b17 | horwell became interested in volcanoes as a child | horwell became interested in volcanoes as a child when she visited mount batur in bali at the age of seven. her undergraduate degree was in environmental science at the university of east anglia, uk, where she studied environmental, earth and public health sciences. she moved to victoria university of wellington for he... | wikipedia |
31a9f277432af049aac9b623063721db5f6822c0 | claire judith horwell is a professor of geohealth | claire judith horwell is a professor of geohealth in the department of earth sciences and institute of hazard, risk and resilience at durham university and the founding director of the international volcanic health hazard network (ivhhn). she studies the health hazards of natural and industrial mineral dusts and commun... | wikipedia |
977cea89bca0c73777633193f010128442ad3809 | electronic system level (esl) design and verification is | electronic system level (esl) design and verification is an electronic design methodology, focused on higher abstraction level concerns. the term electronic system level or esl design was first defined by gartner dataquest, an eda-industry-analysis firm, on february 1, 2001. it is defined in esl design and verification... | wikipedia |
e61834c44e872eb254b90f1b74169230d7624679 | in esl design and verification, verification testing is | in esl design and verification, verification testing is used to prove the integrity of the design of the system or device. numerous verification techniques may be applied; these test methods are usually modified or customized to better accommodate the system or device under test. common esl verification methods include... | wikipedia |
5fa82b3aed12b2aa1bf3bf6d7cfd85dd24454e61 | other tools support import and export or intercommunication | other tools support import and export or intercommunication with components modelled at other levels of abstraction. for instance, an rtl component be converted into a systemc model using vtoc or verilator. and high level synthesis can be used to convert c models of a component into an rtl implementation. | wikipedia |
ce458ccf4d3c46824e73cb89b0b59a5f1d462872 | there are various types of eda tool used | there are various types of eda tool used for esl design. the key component is the virtual platform which is essentially a simulator. the virtual platform most commonly supports transaction-level modeling (tlm), where operations of one component on another are modelled with a simple method call between the objects model... | wikipedia |
6176f22d3189b35ca76c57162ad3f5d59b7f46b5 | esl is an established approach at many of | esl is an established approach at many of the world’s leading system-on-a-chip (soc) design companies, and is being used increasingly in system design. from its genesis as an algorithm modeling methodology with 'no links to implementation', esl is evolving into a set of complementary methodologies that enable embedded ... | wikipedia |
391435da30cca50ba2da809d988b18c3cb3db0cd | the basic premise is to model the behavior | the basic premise is to model the behavior of the entire system using a low-level language such as c, c++, or using graphical "model-based" design tools. newer languages are emerging that enable the creation of a model at a higher level of abstraction including general purpose system design languages like sysml as well... | wikipedia |
cfb79b32139ff70a108424bcc763a039e9f4f365 | electronic system level (esl) design and verification is | electronic system level (esl) design and verification is an electronic design methodology, focused on higher abstraction level concerns. the term electronic system level or esl design was first defined by gartner dataquest, an eda-industry-analysis firm, on february 1, 2001. it is defined in esl design and verification... | wikipedia |
c492ff817763b3cd3bb7d8a674ea5bf6ee263b4d | in mathematics, a commutative ring is a ring | in mathematics, a commutative ring is a ring in which the multiplication operation is commutative. the study of commutative rings is called commutative algebra. complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. this distinction results from the high numb... | wikipedia |
138806d864b3592cbcf1f629e30a5490b3cc6cf9 | a simplicial commutative ring is a simplicial object | a simplicial commutative ring is a simplicial object in the category of commutative rings. they are building blocks for (connective) derived algebraic geometry. a closely related but more general notion is that of e -ring. | wikipedia |
5cc6265c10df3b929ea775c81a139837a4bf4f44 | r is called a commutative differential graded algebra | r is called a commutative differential graded algebra (cdga). an example is the complex of differential forms on a manifold, with the multiplication given by the exterior product, is a cdga. the cohomology of a cdga is a graded-commutative ring, sometimes referred to as the cohomology ring. a broad range examples of gr... | wikipedia |
5ade6be7fde471e18a21deaa2ab30fc26e03eaf1 | by wedderburn's theorem, every finite division ring is | by wedderburn's theorem, every finite division ring is commutative, and therefore a finite field. another condition ensuring commutativity of a ring, due to jacobson, is the following: for every element r of r there exists an integer n > 1 such that r = r. if, r = r for every r, the ring is called boolean ring. more ge... | wikipedia |
911fc78bb4235d0b4477eeb22682c701d079a949 | is only right exact. if it is exact, | is only right exact. if it is exact, m is called flat. if r is local, any finitely presented flat module is free of finite rank, thus projective. despite being defined in terms of homological algebra, flatness has profound geometric implications. for example, if an r -algebra s is flat, the dimensions of the fibers | wikipedia |
4f2f92773b6d9e8864b123657987e6e51e4c3124 | vanishes for all large enough n. moreover, the | vanishes for all large enough n. moreover, the dimensions of these ext-groups, known as betti numbers, grow polynomially in n if and only if r is a local complete intersection ring. a key argument in such considerations is the koszul complex, which provides an explicit free resolution of the residue field k of a local ... | wikipedia |
d8d75bc24039022e1cfd4a9ed45c4f905221647d | the latter functor is exact if m is | the latter functor is exact if m is projective, but not otherwise: for a surjective map e → f of r -modules, a map m → f need not extend to a map m → e. the higher ext functors measure the non-exactness of the hom-functor. the importance of this standard construction in homological algebra stems can be seen from the fa... | wikipedia |
42ee2de911aede2116f376e120797fd2e9c21e8c | projective modules can be defined to be the | projective modules can be defined to be the direct summands of free modules. if r is local, any finitely generated projective module is actually free, which gives content to an analogy between projective modules and vector bundles. the quillen–suslin theorem asserts that any finitely generated projective module over k ... | wikipedia |
8e27b6fd922c5ac53406922dbe109249f01215c2 | if i is an ideal in a commutative | if i is an ideal in a commutative ring r, the powers of i form topological neighborhoods of 0 which allow r to be viewed as a topological ring. this topology is called the i -adic topology. r can then be completed with respect to this topology. formally, the i -adic completion is the inverse limit of the rings r / i. f... | wikipedia |
81d8c2ad9d1b4a5563ab00df13707155b555904a | there are several ways to construct new rings | there are several ways to construct new rings out of given ones. the aim of such constructions is often to improve certain properties of the ring so as to make it more readily understandable. for example, an integral domain that is integrally closed in its field of fractions is called normal. this is a desirable proper... | wikipedia |
900f5b7145b8dcf2a54db894bae28e1a2e0d7682 | holds. a local ring in which equality takes | holds. a local ring in which equality takes place is called a cohen–macaulay ring. local complete intersection rings, and a fortiori, regular local rings are cohen–macaulay, but not conversely. cohen–macaulay combine desirable properties of regular rings (such as the property of being universally catenary rings, which ... | wikipedia |
a9407cc91058eee9020f0620107b093e9c7901a0 | a ring r is a set-theoretic complete intersection | a ring r is a set-theoretic complete intersection if the reduced ring associated to r, i.e., the one obtained by dividing out all nilpotent elements, is a complete intersection. as of 2017, it is in general unknown, whether curves in three-dimensional space are set-theoretic complete intersections. | wikipedia |
2b0b426bb76ba9d54711cdd6453c2bd4e6169e53 | is at least r − n. a ring | is at least r − n. a ring r is called a complete intersection ring if it can be presented in a way that attains this minimal bound. this notion is also mostly studied for local rings. any regular local ring is a complete intersection ring, but not conversely. | wikipedia |
bbdeb696131f6b9f8ac8b94acb5308b68229ee7e | discrete valuation rings are equipped with a function | discrete valuation rings are equipped with a function which assign an integer to any element r. this number, called the valuation of r can be informally thought of as a zero or pole order of r. discrete valuation rings are precisely the one-dimensional regular local rings. for example, the ring of germs of holomorphic ... | wikipedia |
89251c851fa535f11d97b56d15346f19cb35ab45 | holds true, reflecting the idea that the cotangent | holds true, reflecting the idea that the cotangent (or equivalently the tangent) space has at least the dimension of the space spec r. if equality holds true in this estimate, r is called a regular local ring. a noetherian local ring is regular if and only if the ring (which is the ring of functions on the tangent cone... | wikipedia |
a3a8fad4d74d582d66f3163dc25460eacdad33e7 | the k -vector space m / m is | the k -vector space m / m is an algebraic incarnation of the cotangent space. informally, the elements of m can be thought of as functions which vanish at the point p, whereas m contains the ones which vanish with order at least 2. for any noetherian local ring r, the inequality | wikipedia |
9e0f8dbb294ce0137ae4f6065d905c4719786161 | at a prime ideal p is local. this | at a prime ideal p is local. this localization reflects the geometric properties of spec r "around p ". several notions and problems in commutative algebra can be reduced to the case when r is local, making local rings a particularly deeply studied class of rings. the residue field of r is defined as | wikipedia |
57c2cda5f76200672793200adb2bff84f96fdae8 | an r -algebra s is called finitely generated | an r -algebra s is called finitely generated (as an algebra) if there are finitely many elements s,..., s such that any element of s is expressible as a polynomial in the s. equivalently, s is isomorphic to | wikipedia |
bf19bcc17f3fe9ecb62ee7eeaef020ed2afeec1f | commutative rings, together with ring homomorphisms, form a | commutative rings, together with ring homomorphisms, form a category. the ring z is the initial object in this category, which means that for any commutative ring r, there is a unique ring homomorphism z → r. by means of this map, an integer n can be regarded as an element of r. for example, the binomial formula | wikipedia |
2f44020690cf29d132537ea098fba51de7c52e09 | the kernel and image of f are defined | the kernel and image of f are defined by ker(f) = { r ∈ r, f (r) = 0} and im(f) = f (r) = { f (r), r ∈ r }. the kernel is an ideal of r, and the image is a subring of s. | wikipedia |
57e7e1223bf63f38f8f7249f4d81c67f32225f4c | these conditions ensure f (0) = 0. similarly | these conditions ensure f (0) = 0. similarly as for other algebraic structures, a ring homomorphism is thus a map that is compatible with the structure of the algebraic objects in question. in such a situation s is also called an r -algebra, by understanding that s in s may be multiplied by some r of r, by setting | wikipedia |
e14a67b9966ae49c1a975bdb0977b3ff80d1d016 | for example, a field is zero-dimensional, since the | for example, a field is zero-dimensional, since the only prime ideal is the zero ideal. the integers are one-dimensional, since chains are of the form (0) ⊊ (p), where p is a prime number. for non-noetherian rings, and also non-local rings, the dimension may be infinite, but noetherian local rings have finite dimension... | wikipedia |
74926209d0b35c7b8f735fac65efcb6636a9c5fa | the krull dimension (or dimension) dim r of | the krull dimension (or dimension) dim r of a ring r measures the "size" of a ring by, roughly speaking, counting independent elements in r. the dimension of algebras over a field k can be axiomatized by four properties: | wikipedia |
b9d30b1418c0c6c6fb55fd454a70bda5c136fb86 | similar to the fact that manifolds are locally | similar to the fact that manifolds are locally given by open subsets of r, affine schemes are local models for schemes, which are the object of study in algebraic geometry. therefore, several notions concerning commutative rings stem from geometric intuition. | wikipedia |
c4bd43ac21bfb0fdfc47706ab09a9ef6e6c8f82b | the notion of a spectrum is the common | the notion of a spectrum is the common basis of commutative algebra and algebraic geometry. algebraic geometry proceeds by endowing spec r with a sheaf o {\displaystyle {\mathcal {o}}} (an entity that collects functions defined locally, i.e. on varying open subsets). the datum of the space and the sheaf is called an af... | wikipedia |
c6d88dd3700488c287d91d5862e98a243f6d45a5 | thus, maximal ideals reflect the geometric properties of | thus, maximal ideals reflect the geometric properties of solution sets of polynomials, which is an initial motivation for the study of commutative rings. however, the consideration of non-maximal ideals as part of the geometric properties of a ring is useful for several reasons. for example, the minimal prime ideals (i... | wikipedia |
fe8f4fb76de48de19c43e792b2ef2050c494ab4a | interpreting f {\displaystyle f} as a function that | interpreting f {\displaystyle f} as a function that takes the value f mod p (i.e., the image of f in the residue field r / p), this subset is the locus where f is non-zero. the spectrum also makes precise the intuition that localisation and factor rings are complementary: the natural maps r → r and r → r / fr correspon... | wikipedia |
239317393a17c36dff043872e555b230ecd6a341 | the spectrum of a ring r {\displaystyle r}, | the spectrum of a ring r {\displaystyle r}, denoted by spec r {\displaystyle {\text{spec}}\ r}, is the set of all prime ideals of r {\displaystyle r}. it is equipped with a topology, the zariski topology, which reflects the algebraic properties of r {\displaystyle r}: a basis of open subsets is given by | wikipedia |
2b28675f147d041fa2870aa916ecdccfe6b9f57d | any maximal ideal is a prime ideal or, | any maximal ideal is a prime ideal or, more briefly, is prime. moreover, an ideal i {\displaystyle i} is prime if and only if the factor ring r / i {\displaystyle r/i} is an integral domain. proving that an ideal is prime, or equivalently that a ring has no zero-divisors can be very difficult. yet another way of expres... | wikipedia |
0076615470e8dface4fae8bac37d3088f10a49bb | prime ideals, as opposed to prime elements, provide | prime ideals, as opposed to prime elements, provide a way to circumvent this problem. a prime ideal is a proper (i.e., strictly contained in r {\displaystyle r}) ideal p {\displaystyle p} such that, whenever the product a b {\displaystyle ab} of any two ring elements a {\displaystyle a} and b {\displaystyle b} is in p,... | wikipedia |
771d11b9184129acce09f26c291980c6b3f65d82 | becomes stationary eventually. despite the two conditions appearing | becomes stationary eventually. despite the two conditions appearing symmetric, noetherian rings are much more general than artinian rings. for example, z {\displaystyle \mathbb {z} } is noetherian, since every ideal can be generated by one element, but is not artinian, as the chain | wikipedia |
9bf4588cee7260809572ee780e4067c54c4cc1ec | being noetherian is a highly important finiteness condition, | being noetherian is a highly important finiteness condition, and the condition is preserved under many operations that occur frequently in geometry. for example, if r {\displaystyle r} is noetherian, then so is the polynomial ring r {\displaystyle r\left} (by hilbert's basis theorem), any localization s − 1 r {\display... | wikipedia |
22f351c0ae0731cf60f6174a5ca114fdbf0d9c07 | becomes stationary, i.e. becomes constant beyond some index | becomes stationary, i.e. becomes constant beyond some index n {\displaystyle n}. equivalently, any ideal is generated by finitely many elements, or, yet equivalent, submodules of finitely generated modules are finitely generated. | wikipedia |
a9d02846808d6cce914ae20153ab354582946ad7 | an ideal is proper if it is strictly | an ideal is proper if it is strictly smaller than the whole ring. an ideal that is not strictly contained in any proper ideal is called maximal. an ideal m {\displaystyle m} is maximal if and only if r / m {\displaystyle r/m} is a field. except for the zero ring, any ring (with identity) possesses at least one maximal ... | wikipedia |
ef6f1d167db86d4443d67300d0af48621c2b1899 | for example, the ring z / n z | for example, the ring z / n z {\displaystyle \mathbb {z} /n\mathbb {z} } (also denoted z n {\displaystyle \mathbb {z} _{n}}), where n {\displaystyle n} is an integer, is the ring of integers modulo n {\displaystyle n}. it is the basis of modular arithmetic. | wikipedia |
f63469fb52d62b563d3ce3c9b703a153d7423d22 | the definition of ideals is such that "dividing" | the definition of ideals is such that "dividing" i {\displaystyle i} "out" gives another ring, the factor ring r / i {\displaystyle r/i}: it is the set of cosets of i {\displaystyle i} together with the operations | wikipedia |
c3849077e6bf60c064decee6765642fb352492e7 | an element a {\displaystyle a} is a prime | an element a {\displaystyle a} is a prime element if whenever a {\displaystyle a} divides a product b c {\displaystyle bc}, a {\displaystyle a} divides b {\displaystyle b} or c {\displaystyle c}. in a domain, being prime implies being irreducible. the converse is true in a unique factorization domain, but false in gene... | wikipedia |
41bd5d6f168f8ca0dbd52a2d743b2889b9696dd5 | is by either b {\displaystyle b} or c | is by either b {\displaystyle b} or c {\displaystyle c} being a unit. an example, important in field theory, are irreducible polynomials, i.e., irreducible elements in k {\displaystyle k\left}, for a field k {\displaystyle k}. the fact that z {\displaystyle \mathbb {z} } is a ufd can be stated more elementarily by sayi... | wikipedia |
b22ddabc5c9e2ab4d1c7d5ea679601f0bb2cec39 | unlike for general rings, for a principal ideal | unlike for general rings, for a principal ideal domain, the properties of individual elements are strongly tied to the properties of the ring as a whole. for example, any principal ideal domain r {\displaystyle r} is a unique factorization domain (ufd) which means that any element is a product of irreducible elements, ... | wikipedia |
5a72bbbc0ed6297fa5478db6d2e29ee70ac6805f | if f {\displaystyle f} consists of a single | if f {\displaystyle f} consists of a single element r {\displaystyle r}, the ideal generated by f {\displaystyle f} consists of the multiples of r {\displaystyle r}, i.e., the elements of the form r s {\displaystyle rs} for arbitrary elements s {\displaystyle s}. such an ideal is called a principal ideal. if every idea... | wikipedia |
380f616512f1b0efed8daf6922bfdce7e6ca34ff | any ring has two ideals, namely the zero | any ring has two ideals, namely the zero ideal { 0 } {\displaystyle \left\{0\right\}} and r {\displaystyle r}, the whole ring. these two ideals are the only ones precisely if r {\displaystyle r} is a field. given any subset f = { f j } j ∈ j {\displaystyle f=\left\{f_{j}\right\}_{j\in j}} of r {\displaystyle r} (where ... | wikipedia |
e1fca75eac6a2c853649e9f38761f15db4bb35a6 | ideals of a ring r {\displaystyle r} are | ideals of a ring r {\displaystyle r} are the submodules of r {\displaystyle r}, i.e., the modules contained in r {\displaystyle r}. in more detail, an ideal i {\displaystyle i} is a non-empty subset of r {\displaystyle r} such that for all r {\displaystyle r} in r {\displaystyle r}, i {\displaystyle i} and j {\displays... | wikipedia |
887cd11883c97a893bbd1fb8d47c8b8c8e8e225a | a module of finite type is a module | a module of finite type is a module that has a finite spanning set. modules of finite type play a fundamental role in the theory of commutative rings, similar to the role of the finite-dimensional vector spaces in linear algebra. in particular, noetherian rings (see also § noetherian rings, below) can be defined as the... | wikipedia |
7b22ef1baaa23e605b1aabe181e7f191245265e2 | the study of modules is significantly more involved | the study of modules is significantly more involved than the one of vector spaces, since there are modules that do not have any basis, that is, do not contain a spanning set whose elements are linearly independents. a module that has a basis is called a free module, and a submodule of a free module needs not to be free... | wikipedia |
5b88a6b6b17804e108fac7b3a54cb50cc59d3c27 | for a ring r {\displaystyle r}, an r | for a ring r {\displaystyle r}, an r {\displaystyle r} - module m {\displaystyle m} is like what a vector space is to a field. that is, elements in a module can be added; they can be multiplied by elements of r {\displaystyle r} subject to the same axioms as for a vector space. | wikipedia |
d0ac6055b727aabcaf4384ff0102f3d391484631 | subject to certain rules that mimic the cancellation | subject to certain rules that mimic the cancellation familiar from rational numbers. indeed, in this language q {\displaystyle \mathbb {q} } is the localization of z {\displaystyle \mathbb {z} } at all nonzero integers. this construction works for any integral domain r {\displaystyle r} instead of z {\displaystyle \mat... | wikipedia |
9a64cb46ac3692186c79681ad88aa42fa727c705 | the localization of a ring is a process | the localization of a ring is a process in which some elements are rendered invertible, i.e. multiplicative inverses are added to the ring. concretely, if s {\displaystyle s} is a multiplicatively closed subset of r {\displaystyle r} (i.e. whenever s, t ∈ s {\displaystyle s,t\in s} then so is s t {\displaystyle st}) th... | wikipedia |
1620a0ecb97fe30de678eeba1d68c1225d70e2f5 | in contrast to fields, where every nonzero element | in contrast to fields, where every nonzero element is multiplicatively invertible, the concept of divisibility for rings is richer. an element a {\displaystyle a} of ring r {\displaystyle r} is called a unit if it possesses a multiplicative inverse. another particular type of element is the zero divisors, i.e. an eleme... | wikipedia |
dd3fd837738ca840783578270064154ef5d48b24 | if v {\displaystyle v} is some topological space, | if v {\displaystyle v} is some topological space, for example a subset of some r n {\displaystyle \mathbb {r} ^{n}}, real- or complex-valued continuous functions on v {\displaystyle v} form a commutative ring. the same is true for differentiable or holomorphic functions, when the two concepts are defined, such as for v... | wikipedia |
0ab6b8f131011b7d5ef61fb058955debe9c31d9d | if r {\displaystyle r} is a given commutative | if r {\displaystyle r} is a given commutative ring, then the set of all polynomials in the variable x {\displaystyle x} whose coefficients are in r {\displaystyle r} forms the polynomial ring, denoted r {\displaystyle r\left}. the same holds true for several variables. | wikipedia |
c9edd0f488499286cf3ae4f13bc2f5e51e8b5527 | a field is a commutative ring where 0 | a field is a commutative ring where 0 ≠ 1 {\displaystyle 0\not =1} and every non-zero element a {\displaystyle a} is invertible; i.e., has a multiplicative inverse b {\displaystyle b} such that a ⋅ b = 1 {\displaystyle a\cdot b=1}. therefore, by definition, any field is a commutative ring. the rational, real and comple... | wikipedia |
b141103b1e6b67af912cb2f9b1c8981b8bc89409 | an important example, and in some sense crucial, | an important example, and in some sense crucial, is the ring of integers z {\displaystyle \mathbb {z} } with the two operations of addition and multiplication. as the multiplication of integers is a commutative operation, this is a commutative ring. it is usually denoted z {\displaystyle \mathbb {z} } as an abbreviatio... | wikipedia |
8faf7eeb3eba9a25b1bf452785f0da9f198244ee | a ring is a set r {\displaystyle r} | a ring is a set r {\displaystyle r} equipped with two binary operations, i.e. operations combining any two elements of the ring to a third. they are called addition and multiplication and commonly denoted by " + {\displaystyle +} " and " ⋅ {\displaystyle \cdot } "; e.g. a + b {\displaystyle a+b} and a ⋅ b {\displaystyl... | wikipedia |
c492ff817763b3cd3bb7d8a674ea5bf6ee263b4d | in mathematics, a commutative ring is a ring | in mathematics, a commutative ring is a ring in which the multiplication operation is commutative. the study of commutative rings is called commutative algebra. complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. this distinction results from the high numb... | wikipedia |
703f453119a0a5569d44f262410d8e6c27bf0d7e | david k. littman is an american former ice | david k. littman is an american former ice hockey goaltender. he played three games in the national hockey league: two with the buffalo sabres and one with the tampa bay lightning between 1991 and 1993. the rest of his career, which lasted from 1989 to 2000, was mainly spent in the minor international hockey league. he... | wikipedia |
c1f536ac5dd42a2a6704f3aee45d6705ca9aa7f0 | as a result of his successful stints with | as a result of his successful stints with the atlanta knights, littman was selected to compete with team usa at the 1994 iihf world championship, where they finished fourth in the tournament. before his retirement, littman played with the ihl's orlando solar bears, recording 53 wins over two years before a career-endin... | wikipedia |
38ab3198d6d2af5920acf653d3eb425da599d2a5 | on august 28, 1992, littman signed with the | on august 28, 1992, littman signed with the new nhl expansion team, the tampa bay lightning. although he began the season in the minor leagues with the atlanta knights, littman was recalled to the nhl in november 1992. his stay in the national hockey league was short-lived and he was reassigned to the ihl. he became a ... | wikipedia |
809dbdc49cdfb410404c4749da5eca3034dcb750 | littman attended the sabres training camp but was | littman attended the sabres training camp but was reassigned to their international hockey league (ihl) affiliate, the rochester americans, to begin the 1989–90 season. however, the 1990–91 would prove to be a breakout season for him. on january 29, 1991, littman made his nhl debut by replacing darcy wakaluk in the sec... | wikipedia |
6c500477ca4ed9c1f10f28b0426b7e9e027161da | littman spent four years at boston college studying | littman spent four years at boston college studying communications. in his senior year, littman served as one of three captains on the team as the eagles qualified for the ncaa final eight. he ended his season with.912 saves and a.895 percentage. in 2000, his bc record of 2,548 career saves was broken by scott clemmens... | wikipedia |
cb686f65e0c3bc38a8a43f9f2507863ee03330c0 | david k. littman (born june 13, 1967) is | david k. littman (born june 13, 1967) is an american former ice hockey goaltender. he played three games in the national hockey league: two with the buffalo sabres and one with the tampa bay lightning between 1991 and 1993. the rest of his career, which lasted from 1989 to 2000, was mainly spent in the minor internatio... | wikipedia |
145b0fd3915ba07382ce2106908d9848ad1b2ef4 | epimedium, also known as barrenwort, bishop's hat, fairy | epimedium, also known as barrenwort, bishop's hat, fairy wings, horny goat weed, or yin yang huo, is a genus of flowering plants in the family berberidaceae. the majority of the species are endemic to china, with smaller numbers elsewhere in asia, and a few in the mediterranean region. epimedium species are deciduous o... | wikipedia |
c06cf3fea4d6bff3a8d1d42ccb829fd2184b8761 | epimedium wushanense contains a number of flavonoids. 37 | epimedium wushanense contains a number of flavonoids. 37 compounds were characterized from the underground and aerial parts of the plant. among them, 28 compounds were prenylflavonoids. the predominant flavonoid, epimedin c, ranged from 1.4 to 5.1% in aerial parts and 1.0 to 2.8% in underground parts. | wikipedia |
387cc7478b2f0485a658fb159f883a9af8522f63 | while they can be successfully propagated in early | while they can be successfully propagated in early spring, epimediums are best divided in late summer, with the aim of promoting rapid re-growth of roots and shoots before the onset of winter. several breeders (in particular darrell diano probst, tim branney & robin white) have also undertaken their own hybridization p... | wikipedia |
7e288c4cae86f3163b8d6f248ba76dc061b26883 | some varieties and hybrids have been in western | some varieties and hybrids have been in western cultivation for the last 100 to 150 years. there is now a wide array of new chinese species being cultivated in the west, many of which have only recently been discovered, and some of which have yet to be named. there are also many older japanese hybrids and forms, extend... | wikipedia |
c12785472df00854a73f6a72c36e64df5274d316 | the genus was given its name by carl | the genus was given its name by carl linnaeus in 1753, in describing the european species e. alpinum. the name is a latinized version of a greek name for an unidentifiable plant, epimedion, that is mentioned in pliny's natural history (xxvii.57). the meaning of the original name is unclear. | wikipedia |
af1b032d0119342c90c67c98c3b9bfcf5bb649e2 | individual flowers have parts in fours. there are | individual flowers have parts in fours. there are four smaller outer sepals, usually greenish and shed when the flower opens. moving inwards, these are followed by four larger petal-like inner sepals, often brightly coloured. inside the sepals are four true petals. these may be small and flat, but often have a complex ... | wikipedia |
25b218b75e0facb882ef35d562eaca405041f2f3 | species of epimedium are herbaceous perennials, growing from | species of epimedium are herbaceous perennials, growing from an underground rhizome. their growth habits are somewhat variable. some have solitary stems, others have a "tufted" habit, with multiple stems growing close together. there may be several leaves to a stem or the leaves may be solitary, produced from the base ... | wikipedia |
90bcb3134ff6c19cb4276fb60a7dacdfaba8a905 | the species used as a dietary supplement is | the species used as a dietary supplement is epimedium grandiflorum. it contains icariin, which is a weak pde5 inhibitor, in vitro. its clinical effects are unknown. while there is little clinical evidence to date, as sildenafil, vardenafil, and tadalafil – sold under the brand names viagra, levitra and cialis – are all... | wikipedia |
e78501d6d90b2d77179d0945cdf8884c60095171 | epimedium, also known as barrenwort, bishop's hat, fairy | epimedium, also known as barrenwort, bishop's hat, fairy wings, horny goat weed, or yin yang huo (chinese: 淫羊藿; pinyin: yínyánghùo; wade–giles: yin²-yang²-huo⁴), is a genus of flowering plants in the family berberidaceae. the majority of the species are endemic to china, with smaller numbers elsewhere in asia, and a fe... | wikipedia |
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