change of base of fields
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From: Rupert on 24 Jul 2010 02:26 Suppose that k is a field and that k' and F are extensions of k. Does anyone know where I can read the proof that, in the tensor product over k of F with k', prime ideals are minimal?
From: Hagen on 27 Jul 2010 06:00
> Suppose that k is a field and that k' and F are > extensions of k. Does > anyone know where I can read the proof that, in the > tensor product > over k of F with k', prime ideals are minimal? This statement is not true: the tensor product of two rational function fields in one variable over k is a domain but not a field. Hence there exist non-minimal prime ideals. H |