commutative field
1Commutative 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 …
2Field (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 …
3Commutative 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… …
4Field 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… …
5field — /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… …
6Field 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… …
7Field 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.… …
8field — 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 …
9field — 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 …
10field 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… …
