(a) Let L and M be intermediate fields of the extension K F, of finite dimension...
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(a) Let L and M be intermediate fields of the extension K ⊂ F, of finite dimension over K. Assume that [LM : K] = [L : K][M : K] and prove that L ∩ M = K.
(b) The converse of (a) holds if [L : K] or [M : K] is 2.
(c) Using a real and a nonreal cube root of 2 give an example where L ∩ M = K, [L : K] = [M : K] = 3, but [LM : K] < 9.
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ANSWER a Let be an element of L M Since L and M are both intermediate fields of the extension K F be...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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