If F is a splitting field over K of S, then F is also a splitting field over K of the set T of all irreducible factors of polynomials in S.
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A splitting field of a set of polynomials over a field K is an extension field F of K in which each polynomial in the set splits into linear factors, and F is generated by the roots of these polynomials. An irreducible factor of a polynomial in S is a factor that Show more…
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