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On the minimal prime ideals of a tensor product of two fields

Published online by Cambridge University Press:  24 October 2008

P. Vámos
P. Vámos
Affiliation:
University of Sheffield
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Extract

Let F be a field, L a commutative F-algebra and K an extension field of F. An important area of commutative algebra is the study of the passage from L to the k-algebra K ⊗FL, i.e. the investigation of the behaviour of the ideals of L under ‘extension of scalars’. In most problems of this kind one finds that the problem is reduced to the case when the algebra L is itself an extension field of F. It is for this reason that tensor products of fields play an important role (see, for example, (2), chap, viii, (3), (5), (9) and (12), vol. I).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 25 - 35
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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