- algebra over a field
- матем.алгебра над полем
English-Russian scientific dictionary. 2008.
algebra over a field
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Algebra over a field — This article is about a particular kind of vector space. For other uses of the term algebra , see algebra (disambiguation). In mathematics, an algebra over a field is a vector space equipped with a bilinear vector product. That is to say, it is… … Wikipedia
Algebra (disambiguation) — Algebra is a branch of mathematics.Algebra may also mean: * elementary algebra * abstract algebra * linear algebra * universal algebra * computer algebraIn addition, many mathematical objects are known as algebras. * In logic: ** Boolean algebra… … Wikipedia
Algebra — This article is about the branch of mathematics. For other uses, see Algebra (disambiguation). Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from… … Wikipedia
Algebra (ring theory) — In mathematics, specifically in ring theory, an algebra over a commutative ring is a generalization of the concept of an algebra over a field, where the base field K is replaced by a commutative ring R .Any ring can be thought of as an algebra… … Wikipedia
algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… … Universalium
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
Field of sets — Set algebra redirects here. For the basic properties and laws of sets, see Algebra of sets. In mathematics a field of sets is a pair where X is a set and is an algebra over X i.e., a non empty subset of the power set of X closed under the… … 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 with one element — In mathematics, the field with one element is a suggestive name for an object that should exist: many objects in math have properties analogous to objects over a field with q elements, where q = 1, and the analogy between number fields and… … Wikipedia
Algebra homomorphism — A homomorphism between two algebras over a field K , A and B , is a map F:A ightarrow B such that for all k in K and x , y in A ,* F ( kx ) = kF ( x )* F ( x + y ) = F ( x ) + F ( y )* F ( xy ) = F ( x ) F ( y )If F is bijective then F is said to … Wikipedia
*-algebra — * ring= In mathematics, a * ring is an associative ring with a map * : A rarr; A which is an antiautomorphism, and an involution.More precisely, * is required to satisfy the following properties: * (x + y)^* = x^* + y^* * (x y)^* = y^* x^* * 1^* … Wikipedia
