20 relations: Acta Arithmetica, Brauer's theorem on forms, Characteristic (algebra), Elsevier, Emil Artin, Finite field, Guy Terjanian, Hensel's lemma, James Ax, Jan Denef, Jean-Louis Colliot-Thélène, Laurent series, Mathematical logic, Model theory, P-adic number, Quasi-algebraically closed field, Serge Lang, Simon B. Kochen, Ultraproduct, Valuation (algebra).
Acta Arithmetica
Acta Arithmetica is a scientific journal of mathematics publishing papers on number theory.
New!!: Ax–Kochen theorem and Acta Arithmetica · See more »
Brauer's theorem on forms
In mathematics, Brauer's theorem, named for Richard Brauer, is a result on the representability of 0 by forms over certain fields in sufficiently many variables.
New!!: Ax–Kochen theorem and Brauer's theorem on forms · See more »
Characteristic (algebra)
In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.
New!!: Ax–Kochen theorem and Characteristic (algebra) · See more »
Elsevier
Elsevier is an information and analytics company and one of the world's major providers of scientific, technical, and medical information.
New!!: Ax–Kochen theorem and Elsevier · See more »
Emil Artin
Emil Artin (March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent.
New!!: Ax–Kochen theorem and Emil Artin · See more »
Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
New!!: Ax–Kochen theorem and Finite field · See more »
Guy Terjanian
Guy Terjanian is a French mathematician who has worked on algebraic number theory.
New!!: Ax–Kochen theorem and Guy Terjanian · See more »
Hensel's lemma
In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a polynomial equation has a simple root modulo a prime number, then this root corresponds to a unique root of the same equation modulo any higher power of, which can be found by iteratively "lifting" the solution modulo successive powers of.
New!!: Ax–Kochen theorem and Hensel's lemma · See more »
James Ax
James Burton Ax (10 January 1937 – 11 June 2006) was a mathematician who proved several results in algebra and number theory by using model theory.
New!!: Ax–Kochen theorem and James Ax · See more »
Jan Denef
Jan Denef (born 4 September 1951) is a Belgian mathematician.
New!!: Ax–Kochen theorem and Jan Denef · See more »
Jean-Louis Colliot-Thélène
Jean-Louis Colliot-Thélène (born 2 December 1947), is a French mathematician.
New!!: Ax–Kochen theorem and Jean-Louis Colliot-Thélène · See more »
Laurent series
In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree.
New!!: Ax–Kochen theorem and Laurent series · See more »
Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
New!!: Ax–Kochen theorem and Mathematical logic · See more »
Model theory
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.
New!!: Ax–Kochen theorem and Model theory · See more »
P-adic number
In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.
New!!: Ax–Kochen theorem and P-adic number · See more »
Quasi-algebraically closed field
In mathematics, a field F is called quasi-algebraically closed (or C1) if every non-constant homogeneous polynomial P over F has a non-trivial zero provided the number of its variables is more than its degree.
New!!: Ax–Kochen theorem and Quasi-algebraically closed field · See more »
Serge Lang
Serge Lang (May 19, 1927 – September 12, 2005) was a French-born American mathematician and activist.
New!!: Ax–Kochen theorem and Serge Lang · See more »
Simon B. Kochen
Simon Bernhard Kochen (born 14 August 1934, Antwerpen) is a Canadian mathematician, working in the fields of model theory, number theory and quantum mechanics.
New!!: Ax–Kochen theorem and Simon B. Kochen · See more »
Ultraproduct
The ultraproduct is a mathematical construction that appears mainly in abstract algebra and in model theory, a branch of mathematical logic.
New!!: Ax–Kochen theorem and Ultraproduct · See more »
Valuation (algebra)
In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field.
New!!: Ax–Kochen theorem and Valuation (algebra) · See more »
Redirects here:
Ax-Kochen isomorphism theorem, Ax-Kochen theorem, Model theory of valued fields.