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Extension
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19:18
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Introduction to Extension Fields and Splitting Fields in Abstract Algebra
In Abstract Algebra, given a field F, a field extension E of F is a field which contains F as a subfield. Kronecker's Theorem guarantees the existence of an extension field in which a non-constant polynomial f(x) in F[x] has a zero. We say f(x) in F[x] splits in E if, in essence, it completely factors in E[x]. If E is a minimal field extension ...
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