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Tight closure commutes with localization in binomial rings

Author(s): Karen E. Smith
Journal: Proc. Amer. Math. Soc. 129 (2001), 667-669.
MSC (1991): Primary 13A35
Posted: September 19, 2000
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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: 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
Posted: 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
Copyright of article: Copyright 2000, American Mathematical Society

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