A characterization of closure operations that induce big CohenMacaulay modules
Author:
Geoffrey D. Dietz
Journal:
Proc. Amer. Math. Soc. 138 (2010), 38493862
MSC (2000):
Primary 13C14; Secondary 13A35
Published electronically:
May 24, 2010
MathSciNet review:
2679608
Fulltext PDF Free Access
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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 CohenMacaulay module over a complete local domain . Conversely, we show that if such a exists over , then there exists a closure operation that satisfies the given axioms.
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 G. DIETZ, Big CohenMacaulay algebras and seeds, Trans. Amer. Math. Soc. 359 (2007), no. 12, 59595989. MR 2336312 (2008h:13021)
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 M. HOCHSTER, Topics in the homological theory of modules over commutative rings, CBMS Regional Conf. Ser. in Math. 24, Amer. Math. Soc., Providence, RI, 1975. MR 0371879 (51:8096)
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 M. HOCHSTER, Solid closure, in: Commutative Algebra: Syzygies, Multiplicities and Birational Algebra, Contemp. Math. 159, Amer. Math. Soc., Providence, RI, 1994, 103172. MR 1266182 (95a:13011)
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 M. HOCHSTER, Foundations of tight closure theory, lecture notes available at http://www.math.lsa.umich.edu/hochster/mse.html.
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 M. HOCHSTER and C. HUNEKE, Tight closure of parameter ideals and splitting in modulefinite extensions, J. Algebraic Geom. 3 (1994), no. 4, 599670. MR 1297848 (95k:13002)
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 M. HOCHSTER and C. HUNEKE, Tight Closure in Equal Characteristic Zero, preprint available at http://www.math.lsa.umich.edu/ hochster/msr.html.
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 K.E. SMITH, Tight closure of parameter ideals, Invent. Math. 115 (1994), 4160. MR 1248078 (94k:13006)
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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/S000299392010104173
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.
