Let E be a finite extension of F. Let E=E1,E2,...,Er be all the distinct conjugates of E over F. Prove that the composite K=E1E2...Er is the smallest normal extension of F containing E.
Would anyone know how to attempt this problem/solve it?
2026-03-27 07:50:29.1774597829
Smallest normal extension of F containing E is composite of E and all its conjugates over F. Proof
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