(a) For any u 1 , . . . , u n F and any permutation...
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(a) For any u1, . . . , un ϵ F and any permutation σ ϵ Sn, K(u1, . . . , Un) = K(uσ(1),. .. , uσ(n))
(b) K(u1, ... , Un-1)(un) = K(u1, ... , Un).
(c) State and prove the analogues of (a) and (b) for K[u1, ... , Un].
(d) If each ui is algebraic over K, then K(u1, ... , Un) = K[u1, ... , un].
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a Statement For any elements u1 un in a field K and any permutation in the symmetric group Sn the field generated by u1 un is the same as the field ge...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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