Outline of Galois eory Development
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چکیده
. Existence of Splitting Fields for a polynomial or family of polynomials F ⊂ F[X]. Existence of Algebraic Closure. Characterizations of Algebraic Closure: A field E is algebraically closed if every nonconstant polynomial in E[X] factors as a product of linear polynomials. (Equivalently, every nonconstant polynomial in E[X] has a root in E.) A field E is an algebraic closure of a subfield F if E is algebraic over F and every non-constant polynomial in F[X] factors as a product of linear polynomials in E[X].
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تاریخ انتشار 2008