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Noether
Noether is the family name of several mathematicians (particularly, the Noether family), and the name given to some of their mathematical contributions: * Max Noether (1844–1921), father of Emmy and Fritz Noether, and discoverer of: ** Noether inequality ** Max Noether's theorem, several theorems * Emmy Noether (1882–1935), professor at the University of Göttingen and at Bryn Mawr College ** Noether's theorem (or Noether's first theorem) ** Noether's second theorem ** Noether normalization lemma ** Noetherian rings ** Nöther crater, on the far side of the moon, named after Emmy Noether * Fritz Noether (1884–1941), professor at the University of Tomsk * Gottfried E. Noether (1915–1991), son of Fritz Noether, statistician at the University of Connecticut See also * Noether's theorem (other) * List of things named after Emmy Noether Emmy Noether was a German mathematician who flourished in the early 20th century. This article is dedicated to the things n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emmy Noether
Amalie Emmy NoetherEmmy is the ''Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noether'' (1907/08, NR. 2988); reproduced in: ''Emmy Noether, Gesammelte Abhandlungen – Collected Papers,'' ed. N. Jacobson 1983; online facsimile aphysikerinnen.de/noetherlebenslauf.html). Sometimes ''Emmy'' is mistakenly reported as a short form for ''Amalie'', or misreported as "Emily". e.g. (, ; ; 23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She discovered Noether's First and Second Theorem, which are fundamental in mathematical physics. She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as the most important woman in the history of mathematics. As one of the leading mathematicians of her time, she developed some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noetherian Ring
In mathematics, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; if the chain condition is satisfied only for left ideals or for right ideals, then the ring is said left-Noetherian or right-Noetherian respectively. That is, every increasing sequence I_1\subseteq I_2 \subseteq I_3 \subseteq \cdots of left (or right) ideals has a largest element; that is, there exists an such that: I_=I_=\cdots. Equivalently, a ring is left-Noetherian (resp. right-Noetherian) if every left ideal (resp. right-ideal) is finitely generated. A ring is Noetherian if it is both left- and right-Noetherian. Noetherian rings are fundamental in both commutative and noncommutative ring theory since many rings that are encountered in mathematics are Noetherian (in particular the ring of integers, polynomial rings, and rings of algebraic integers in number fields), and many general theorems on rings rely heavily on Noetherian property (for example, the Laskerâ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether's Theorem
Noether's theorem or Noether's first theorem states that every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function, from which the system's behavior can be determined by the principle of least action. This theorem only applies to continuous and smooth symmetries over physical space. Noether's theorem is used in theoretical physics and the calculus of variations. It reveals the fundamental relation between the symmetries of a physical system and the conservation laws. It also made modern theoretical physicists much more focused on symmetries of physical systems. A generalization of the formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cann ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Things Named After Emmy Noether ...
Emmy Noether was a German mathematician who flourished in the early 20th century. This article is dedicated to the things named after her achievements. Mathematics "Noetherian" * Noetherian * Noetherian group * Noetherian module * Noetherian ring * Noetherian space * Noetherian induction * Noetherian scheme Other Astronomy * The crater Nöther on the far side of the Moon is named after her. * The 7001 Noether asteroid also is named for her.Blue, JenniferGazetteer of Planetary Nomenclature USGS. 25 July 2007. Retrieved on 13 April 2008. References {{reflist, 20em nother Amalie Emmy NoetherEmmy is the ''Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noethe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Noether
Max Noether (24 September 1844 – 13 December 1921) was a German mathematician who worked on algebraic geometry and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century". He was the father of Emmy Noether. Biography Max Noether was born in Mannheim in 1844, to a Jewish family of wealthy wholesale hardware dealers. His grandfather, Elias Samuel, had started the business in Bruchsal in 1797. In 1809 the Grand Duchy of Baden established a "Tolerance Edict", which assigned a hereditary surname to the male head of every Jewish family which did not already possess one. Thus the Samuels became the Noether family, and as part of this Christianization of names, their son Hertz (Max's father) became Hermann. Max was the third of five children Hermann had with his wife Amalia Würzburger. At 14, Max contracted polio and was afflicted by its effects for the rest of his life. Through self-study, he learned advanced mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fritz Noether
Fritz Alexander Ernst Noether (7 October 1884 – 10 September 1941) was a Jewish German mathematician who emigrated from Nazi Germany to the Soviet Union. He was later executed by the NKVD. Biography Fritz Noether's father Max Noether was a mathematician and professor in Erlangen. The notable mathematician Emmy Noether was his elder sister. He had two sons, Herman D. Noether and Gottfried E. Noether. His eldest son Herman was a chemist. Gottfried was an American statistician and educator, and wrote a brief biography of his father. Fritz Noether was also an able mathematician. Not allowed to work in Nazi Germany for being a Jew, he moved to the Soviet Union, where he was appointed to a professorship at the Tomsk State University. In November 1937, during the Great Purge, he was arrested at his home in Tomsk by the NKVD. On 23 October 1938, Noether was sentenced to 25 years of imprisonment on charges of espionage and sabotage. He served time in different pris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether's Theorem (other)
Noether's theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. Noether's theorem may also refer to: Theorems by Emmy Noether * Noether's second theorem, on infinite-dimensional Lie algebras and differential equations * Noether normalization lemma, on finitely generated algebra over a field * Noether isomorphism theorems in abstract algebra Theorems by Max Noether * Max Noether's theorem, several theorems ** Noether's theorem on rationality for surfaces ** Noether inequality, a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4-manifold See also * Emmy Noether (1882–1935), German Jewish mathematician * Herglotz–Noether theorem, in special relativity * Lasker–Noether theorem, that states that every Noetherian ring is a Lasker ring * Skolem–Noether theorem, which characterizes the automorphisms of simple rings * Albert–Brauer–Hasse–N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether's Second Theorem
In mathematics and theoretical physics, Noether's second theorem relates symmetries of an action functional with a system of differential equations. :Translated in The action ''S'' of a physical system is an integral of a so-called Lagrangian function ''L'', from which the system's behavior can be determined by the principle of least action. Specifically, the theorem says that if the action has an infinite-dimensional Lie algebra of infinitesimal symmetries parameterized linearly by ''k'' arbitrary functions and their derivatives up to order ''m'', then the functional derivatives of ''L'' satisfy a system of ''k'' differential equations. Noether's second theorem is sometimes used in gauge theory. Gauge theories are the basic elements of all modern field theories of physics, such as the prevailing Standard Model. The theorem is named after Emmy Noether. See also * Noether's first theorem * Noether identities * Gauge symmetry (mathematics) In mathematics, any Lagrangian sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether Family
The Noether family is a family of German mathematicians, whose family name has been given to some of their mathematical contributions: *Max Noether (1844–1921), father of Emmy and Fritz Noether, **Emmy Noether (1882–1935), professor at the University of Göttingen and at Bryn Mawr College **Fritz Noether Fritz Alexander Ernst Noether (7 October 1884 – 10 September 1941) was a Jewish German mathematician who emigrated from Nazi Germany to the Soviet Union. He was later executed by the NKVD. Biography Fritz Noether's father Max Noether ... (1884–1941), professor at the University of Tomsk *** Gottfried E. Noether (1915–1991), son of Fritz Noether See also * Noether's theorem (other) * List of things named after Emmy Noether Scientific families German families {{mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Noether's Theorem (other)
In algebraic geometry, Max Noether's theorem may refer to the results of Max Noether: * Several closely related results of Max Noether on canonical curves * AF+BG theorem, or Max Noether's fundamental theorem, a result on algebraic curves in the projective plane, on the residual sets of intersections * Max Noether's theorem on curves lying on algebraic surfaces, which are hypersurfaces in ''P''3, or more generally complete intersections * Noether's theorem on rationality for surfaces * Max Noether theorem on the generation of the Cremona group by quadratic transformations See also *Noether's theorem, usually referring to a result derived from work of Max's daughter Emmy Noether *Noether inequality *Special divisor *Hirzebruch–Riemann–Roch theorem In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result generalizing the classical Riemann–Roch theorem on Riemann surfaces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether Normalization Lemma
In mathematics, the Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether in 1926. It states that for any field ''k'', and any finitely generated commutative ''k''-algebra ''A'', there exists a non-negative integer ''d'' and algebraically independent elements ''y''1, ''y''2, ..., ''y''''d'' in ''A'' such that ''A'' is a finitely generated module over the polynomial ring ''S'' = ''k'' 'y''1, ''y''2, ..., ''y''''d'' The integer ''d'' above is uniquely determined; it is the Krull dimension of the ring ''A''. When ''A'' is an integral domain, ''d'' is also the transcendence degree of the field of fractions of ''A'' over ''k''. The theorem has a geometric interpretation. Suppose ''A'' is integral. Let ''S'' be the coordinate ring of the ''d''-dimensional affine space \mathbb A^d_k, and let ''A'' be the coordinate ring of some other ''d''-dimensional affine variety ''X''. Then the inclusion map ''S'' → ''A'' induces a surjective f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether Inequality
In mathematics, the Noether inequality, named after Max Noether, is a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4-manifold. It holds more generally for minimal projective surfaces of general type over an algebraically closed field. Formulation of the inequality Let ''X'' be a smooth minimal projective surface of general type defined over an algebraically closed field (or a smooth minimal compact complex surface of general type) with canonical divisor ''K'' = −''c''1(''X''), and let ''p''g = ''h''0(''K'') be the dimension of the space of holomorphic two forms, then : p_g \le \frac c_1(X)^2 + 2. For complex surfaces, an alternative formulation expresses this inequality in terms of topological invariants of the underlying real oriented four manifold. Since a surface of general type is a Kähler surface, the dimension of the maximal positive subspace in intersection form on the second cohomology is given by ''b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
