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

 

On residually $S_2$ ideals and projective dimension one modules


Authors: Alberto Corso and Claudia Polini
Journal: Proc. Amer. Math. Soc. 129 (2001), 1309-1315
MSC (2000): Primary 13A30; Secondary 13B22, 13C10, 13C40
Published electronically: October 25, 2000
MathSciNet review: 1814157
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Abstract:

We prove that certain modules are faithful. This enables us to draw consequences about the reduction number and the integral closure of some classes of ideals.


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Additional Information

Alberto Corso
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Address at time of publication: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: corso@math.msu.edu, corso@ms.uky.edu

Claudia Polini
Affiliation: Department of Mathematics, Hope College, Holland, Michigan 49422
Address at time of publication: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: polini@cs.hope.edu, polini@math.uoregon.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05696-3
PII: S 0002-9939(00)05696-3
Keywords: Residual intersections, $G_s$ properties, reductions and reduction number of ideals, integral closure of ideals, Rees algebras of modules
Received by editor(s): May 18, 1999
Received by editor(s) in revised form: August 29, 1999
Published electronically: October 25, 2000
Additional Notes: Both authors sincerely thank Bernd Ulrich for many helpful discussions they had concerning the material in this paper. The NSF, under grant DMS-9970344, has also partially supported the research of the second author and has therefore her heartfelt thanks.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society