 algebraic 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.
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Universalium. 2010.
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Universalium. 2010.
Algebraic 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.… … Wikipedia
algebraic 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 … Useful english dictionary
simple 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. * * * … Universalium
simple 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 … Useful english dictionary
Algebraic 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… … Wikipedia
Algebraic 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… … Wikipedia
Algebraic 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… … Wikipedia
Extension (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… … Wikipedia
Algebraicgroup 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… … Wikipedia
Algebraic Ktheory — In mathematics, algebraic K theory is an important part of homological algebra concerned with defining and applying a sequence Kn(R) of functors from rings to abelian groups, for all integers n. For historical reasons, the lower K groups K0 and… … Wikipedia