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Tensor products and localizations of algebras

Published online by Cambridge University Press:  22 January 2016

S. R. Bowman  and
L. O’Carroll
S. R. Bowman
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Mayfield Road, EDINBURGH EH9 3JZ
L. O’Carroll
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Mayfield Road, EDINBURGH EH9 3JZ
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In a recent paper [5], it was shown that the tensor product of a finite number of fields over a common subfield satisfies the property that each localization at a prime ideal is a primary ring (in the sense that a zero-divisor is in fact a nilpotent element).

In the first section of this paper, we exploit the properties of associated primes and of flat extensions so as to generalize the above result to zero-dimensional algebras; a simple example shows that this is the best one can hope for. The converse situation is also investigated.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 102 , June 1986 , pp. 155 - 161
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

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