algebraic extension
21Algebraic group — In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. In category theoretic terms, an algebraic group is a… …
22Algebraic differential equation — Note: Differential algebraic equation is something different. In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra. There are several such notions, according to the… …
23Algebraic cycle — In mathematics, an algebraic cycle on an algebraic variety V is, roughly speaking, a homology class on V that is represented by a linear combination of subvarieties of V . Therefore the algebraic cycles on V are the part of the algebraic topology …
24Extension de Kummer — Théorie de Kummer En mathématiques, la théorie de Kummer, ainsi désignée suivant le nom du mathématicien allemand du XIX siècle Ernst Kummer, suite à ses travaux sur le dernier théorème de Fermat, donne une description de certaines extensions d… …
25Algebraic 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 …
26Extension and contraction of ideals — In commutative algebra, the extension and contraction of ideals are operations performed on sets of ideals. Extension of an ideal Let A and B be two commutative rings with unity, and let f : A → B be a (unital) ring homomorphism. If mathfrak{a}… …
27Field 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… …
28Normal extension — In abstract algebra, an algebraic field extension L/K is said to be normal if L is the splitting field of a family of polynomials in K[X]. Bourbaki calls such an extension a quasi Galois extension. Contents 1 Equivalent properties and examples 2… …
29Separable extension — In mathematics, an algebraic field extension L / K is separable if it can be generated by adjoining to K a set each of whose elements is a root of a separable polynomial over K . In that case, each beta; in L has a separable minimal polynomial… …
30Isomorphism extension theorem — In field theory, a branch of mathematics, the isomorphism extension theorem is an important theorem regarding the extension of a field isomorphism to a larger field. Isomorphism extension theorem The theorem states that given any field F, an… …
