algebraic extension
1Algebraic extension — In abstract algebra, a field extension L / K is called algebraic if every element of L is algebraic over K , i.e. if every element of L is a root of some non zero polynomial with coefficients in K . Field extensions which are not algebraic, i.e.… …
2algebraic extension — Math. a field containing a given field such that every element in the first field is algebraic over the given field. Cf. extension field. * * * …
3algebraic extension — Math. a field containing a given field such that every element in the first field is algebraic over the given field. Cf. extension field …
4simple algebraic extension — Math. a simple extension in which the specified element is a root of an algebraic equation in the given field. Cf. simple transcendental extension. * * * …
5simple algebraic extension — Math. a simple extension in which the specified element is a root of an algebraic equation in the given field. Cf. simple transcendental extension …
6Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …
7Algebraic closure — In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics.Using Zorn s lemma, it can be shown that every field has an… …
8Algebraic curve — In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with… …
9Extension (mathematics) — In mathematics, the word extension has many uses. See:Analysis* Carathéodory s extension theorem * Continuous linear extension * M. Riesz extension theorem * Krein extension theorem * Hahn Banach theoremAlgebra* Abelian extension * Algebraic… …
10Algebraic-group factorisation algorithm — Algebraic group factorisation algorithms are algorithms for factoring an integer N by working in an algebraic group defined modulo N whose group structure is the direct sum of the reduced groups obtained by performing the equations defining the… …
