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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of closure operations that induce big Cohen-Macaulay modules


Author: Geoffrey D. Dietz
Journal: Proc. Amer. Math. Soc. 138 (2010), 3849-3862
MSC (2000): Primary 13C14; Secondary 13A35
Published electronically: May 24, 2010
MathSciNet review: 2679608
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Abstract: The intent of this paper is to present a set of axioms that are sufficient for a closure operation to generate a balanced big Cohen-Macaulay module $ B$ over a complete local domain $ R$. Conversely, we show that if such a $ B$ exists over $ R$, then there exists a closure operation that satisfies the given axioms.


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Additional Information

Geoffrey D. Dietz
Affiliation: Department of Mathematics, Gannon University, Erie, Pennsylvania 16541
Email: gdietz@member.ams.org

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10417-3
PII: S 0002-9939(2010)10417-3
Received by editor(s): October 28, 2009
Received by editor(s) in revised form: January 30, 2010
Published electronically: May 24, 2010
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.