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Balanced big Cohen-Macaulay modules and free extensions of local rings

Published online by Cambridge University Press:  14 November 2011

Adrian M. Riley
Adrian M. Riley
Affiliation:
Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, England
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Synopsis

Let A and B be commutative Noetherian local rings, such that B is a finitely generated free A-module. 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 1-2 , 1982 , pp. 41 - 45
Copyright
Copyright © Royal Society of Edinburgh 1982

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References

1Griffith, P.. A representation theorem for complete local rings. J. Pure Appl. Algebra 7 (1976), 303–315.CrossRefGoogle Scholar
2Hochster, M.. Cohen-Macaulay modules. Conference in Commutative Algebra. Lecture Notes in Mathematics 311, pp. 120–152 (Springer, Berlin 1973).Google Scholar
3Hochster, M.. Topics in the homological theory of modules over commutative rings (C.B.M.S. Regional Conference Series in Mathematics No. 24) (Providence, R.I.: AMS, 1975).Google Scholar
4Hochster, M.. Big Cohen-Macaulay modules and algebras and embeddability in rings of Witt vectors. Proceedings of the Conference on Commutative Algebra, Queen's University, Kingston, Ontario, 1975 (Queen's University papers in Pure and Applied Mathematics No. 24, 1975, pp. 106–195).Google Scholar
5Matsumura, H.. Commutative Algebra, 2nd edn (Reading, Mass.: Benjamin-Cummings, 1980).Google Scholar
6Northcott, D. G.. Lessons on Rings, Modules and Multiplicities (London: Cambridge University Press, 1968).CrossRefGoogle Scholar
7Northcott, D. G.. An Introduction to Homological Algebra (London: Cambridge University Press, 1972).Google Scholar
8Sharp, R. Y.. The Cousin complex for a module over a commutative Noetherian ring. Math. Z. 112 (1969), 340–356.Google Scholar
9Sharp, R. Y.. The Cousin complex and integral extensions of Noetherian domains. Proc. Cambridge Philos. Soc. 73 (1973), 407–415.CrossRefGoogle Scholar
10Sharp, R. Y.. Cohen-Macaulay properties for balanced big Cohen-Macaulay modules. Math. Proc. Cambridge Philos. Soc. 90 (1981), 229–238.Google Scholar
11Sharp, R. Y.. A Cousin complex characterisation of balanced big-Cohen-Macaulay modules. Quart. J. Math. Oxford, to appear.Google Scholar