Show that if E is a finite extension of a field F and [E : F] is
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Show that if E is a finite extension of a field F and [E : F] is a prime number, then E is a simple extension of F and, indeed, E = F(α) for every a ∈ E not in F.
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Let be any element in E that is not in F Then E F E FF F p for some prime p by Theorem 314 Because i...View the full answer
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