Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

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

P. Vámosa1

a1 University of Sheffield

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 xs2297F L, 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).

(Received February 08 1977)

(Revised September 26 1977)

(Revised December 09 1977)