In the extension of an infinite field K by K(x,y), the intermediate field K(x) is Galois over
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In the extension of an infinite field K by K(x,y), the intermediate field K(x) is Galois over K, but not stable (relative to K(x,y) and K). [See Exercise 9]
Data from exercise 9
(a) If K is an infinite field, then K(x) is Galois over K.
(b) If K is finite, then K(x) is not Galois over K.
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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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