Let F be an algebraic closure of Z P (p prime). (a) F is algebraic Galois over

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Let F be an algebraic closure of Z^P(p prime).

(a) F is algebraic Galois over Z^P.

(b) The map φ: F→ F given by u| → u^P is a nonidentity Z_p-automorphism of F.

(c) The subgroup H = (φ) is a proper subgroup of Aut_zpF whose fixed field is Z_p, which is also the fixed field of Aut_zPF by (a).

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 16, 2023 03:50 AM

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Let F be an algebraic closure of Z P (p prime). (a) F is algebraic Galois over

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a Let Zpx be an irreducible polynomial with a root u F Since F is algebraic over Zp u is also algebraic over Zp By the theorem of finite fields the ex...View the full answer

Algebra Graduate Texts In Mathematics 73

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