irreducible domain

irreducible domain
мат.
неприводимая область

English-Russian scientific dictionary. 2008.

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  • Domain — may refer to: General Territory (administrative division), a non sovereign geographic area which has come under the authority of another government Public domain, a body of works and knowledge without proprietary interest Eminent domain, the… …   Wikipedia

  • Irreducible polynomial — In mathematics, the adjective irreducible means that an object cannot be expressed as a product of at least two non trivial factors in a given set. See also factorization. For any field F , the ring of polynomials with coefficients in F is… …   Wikipedia

  • Domain (ring theory) — In mathematics, especially in the area of abstract algebra known as ring theory, a domain is a ring such that ab = 0 implies that either a = 0 or b = 0.[1] That is, it is a ring which has no left or right zero divisors. (Sometimes such a ring is… …   Wikipedia

  • irreducible — adjective Date: 1633 1. impossible to transform into or restore to a desired or simpler condition < an irreducible matrix >; specifically incapable of being factored into polynomials of lower degree with coefficients in some given field (as the… …   New Collegiate Dictionary

  • Integral domain — In abstract algebra, an integral domain is a commutative ring that has no zero divisors,[1] and which is not the trivial ring {0}. It is usually assumed that commutative rings and integral domains have a multiplicative identity even though this… …   Wikipedia

  • Unique factorization domain — In mathematics, a unique factorization domain (UFD) is, roughly speaking, a commutative ring in which every element, with special exceptions, can be uniquely written as a product of prime elements, analogous to the fundamental theorem of… …   Wikipedia

  • Dedekind domain — In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily …   Wikipedia

  • Bézout domain — In mathematics, a Bézout domain is an integral domain which is, in a certain sense, a non Noetherian analogue of a principal ideal domain. More precisely, a Bézout domain is a domain in which every finitely generated ideal is principal. A… …   Wikipedia

  • Structure theorem for finitely generated modules over a principal ideal domain — In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that… …   Wikipedia

  • Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

  • Representation theory of finite groups — In mathematics, representation theory is a technique for analyzing abstract groups in terms of groups of linear transformations. See the article on group representations for an introduction. This article discusses the representation theory of… …   Wikipedia


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