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Balanced big Cohen-Macaulay modules and ring extensions

Published online by Cambridge University Press:  14 November 2011

Liam O'Carroll
Liam O'Carroll
Affiliation:
Department of Mathematics, University of Edinburgh, Mayfield Road, Edinburgh EH93JZ
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Extract

Let A and B be commutative Noetherian local rings such that B contains A and B is flat and integral over A. It is shown that if M is a balanced big Cohen-Macaulay A-module (that is, every system of parameters for A is an M-sequence), then M⊗AB is a balanced big Cohen-Macaulay B-module. An example of a ring A is given such that, if B is the completion of A, then the analogous result is false in this case. This answers a question posed by Riley in the negative.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 1-2 , 1984 , pp. 171 - 172
Copyright
Copyright © Royal Society of Edinburgh 1984

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