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commutative field

См. также в других словарях:

  • Commutative ring — In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Some specific kinds of commutative rings are given with …   Wikipedia

  • Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

  • Commutative property — For other uses, see Commute (disambiguation). In mathematics an operation is commutative if changing the order of the operands does not change the end result. It is a fundamental property of many binary operations, and many mathematical proofs… …   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

  • field — /feeld/, n. 1. an expanse of open or cleared ground, esp. a piece of land suitable or used for pasture or tillage. 2. Sports. a. a piece of ground devoted to sports or contests; playing field. b. (in betting) all the contestants or numbers that… …   Universalium

  • Field of definition — In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong. Given polynomials, with coefficients in a field K , it may not be obvious… …   Wikipedia

  • Field axioms — ▪ Table Field axioms axiom 1 Closure: the combination (hereafter indicated by addition or multiplication) of any two elements in the set produces an element in the set. axiom 2 Addition is commutative: a + b = b + a for any elements in the set.… …   Universalium

  • field — I. noun Etymology: Middle English, from Old English feld; akin to Old High German feld field, Old English flōr floor more at floor Date: before 12th century 1. a. (1) an open land area free of woods and buildings (2) an area of land marked by the …   New Collegiate Dictionary

  • field — noun 1》 an area of open land, especially one planted with crops or pasture.     ↘a piece of land used for a sport or game.     ↘a large area of land or water completely covered in snow or ice.     ↘an area rich in a natural product, typically oil …   English new terms dictionary

  • field theory — Physics. a detailed mathematical description of the distribution and movement of matter under the influence of one or more fields. [1900 05] * * * In mathematics, the study of the structure of a set of objects (e.g., numbers) with two combining… …   Universalium

  • field of quotients — Math. a field whose elements are pairs of elements of a given commutative integral domain such that the second element of each pair is not zero. The field of rational numbers is the field of quotients of the integral domain of integers. Also… …   Universalium

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