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

 

Tight closure commutes with localization in binomial rings


Author: Karen E. Smith
Journal: Proc. Amer. Math. Soc. 129 (2001), 667-669
MSC (1991): Primary 13A35
Published electronically: September 19, 2000
MathSciNet review: 1706969
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Abstract: It is proved that tight closure commutes with localization in any domain which has a module finite extension in which tight closure is known to commute with localization. It follows that tight closure commutes with localization in binomial rings, in particular in semigroup or toric rings.


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Additional Information

Karen E. Smith
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: kesmith@math.lsa.umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05626-4
PII: S 0002-9939(00)05626-4
Keywords: Tight closure, localization, binomial ideals, toric rings, semigroup rings
Received by editor(s): January 11, 1999
Received by editor(s) in revised form: May 15, 1999
Published electronically: September 19, 2000
Additional Notes: The author was supported by the National Science Foundation and the Alfred P. Sloan Foundation.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society