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Splitting field proofs

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Let K1 and K2 be finite extensions of F contained in the field K, and assume both are splitting fields over F

1. Prove that their composite K1K2 is splitting field over F.
2. Prove that K1^K1 is a splitting field over F.

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Solution Summary

This provides two splitting field proofs.

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Observe that the join K1K2/F is a field, and moreover it is finite whenever K1/F and K2/F are

to prove (1) let f, g be in F[x] by polynomials such that K1 resp. K2 is a splitting field for f resp. g and ...

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