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单词 AlgebraicallyClosed
释义

algebraically closed


A field K is algebraically closedMathworldPlanetmath if every non-constant polynomialPlanetmathPlanetmath in K[X] has a root in K.

An extension fieldMathworldPlanetmath L of K is an algebraic closure of K if L is algebraically closed and every element of L is algebraic over K. Using the axiom of choiceMathworldPlanetmath, one can show that any field has an algebraic closure. Moreover, any two algebraic closures of a field are isomorphic as fields, but not necessarily canonically isomorphic.

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更新时间:2025/5/4 15:13:49