Перевод: со всех языков на все языки

со всех языков на все языки

algebraically independent set

См. также в других словарях:

  • Algebraic independence — In abstract algebra, a subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non trivial polynomial equation with coefficients in K . This means that for every finite sequence α1, ..., α n of …   Wikipedia

  • Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… …   Wikipedia

  • Lindemann–Weierstrass theorem — In mathematics, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if α1,...,α n are algebraic numbers which are linearly independent over the rational numbers Q, then… …   Wikipedia

  • Inverse Galois problem — In mathematics, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers Q. This problem, first posed in the 19th centuryFact|date=February 2007, is… …   Wikipedia

  • Cluster algebra — Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky (2002, 2003, 2007). A cluster algebra of rank n is an integral domain A, together with some subsets of size n called clusters whose union generates the… …   Wikipedia

  • Transcendence degree — In abstract algebra, the transcendence degree of a field extension L / K is a certain rather coarse measure of the size of the extension. Specifically, it is defined as the largest cardinality of an algebraically independent subset of L over K .A …   Wikipedia

  • Glossary of field theory — Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative ring… …   Wikipedia

  • Transcendence theory — In mathematics, transcendence theory is a branch of number theory that investigates transcendental numbers, in both qualitative and quantitative ways.TranscendenceThe fundamental theorem of algebra tells us that if we have a non zero polynomial… …   Wikipedia

  • Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) …   Wikipedia

  • Elementary symmetric polynomial — In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial P can be expressed as a polynomial in elementary… …   Wikipedia

  • Jordan normal form — In linear algebra, a Jordan normal form (often called Jordan canonical form)[1] of a linear operator on a finite dimensional vector space is an upper triangular matrix of a particular form called Jordan matrix, representing the operator on some… …   Wikipedia

Поделиться ссылкой на выделенное

Прямая ссылка:
Нажмите правой клавишей мыши и выберите «Копировать ссылку»