On residually 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

DOI:
https://doi.org/10.1090/S0002-9939-00-05696-3

Published electronically:
October 25, 2000

MathSciNet review:
1814157

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-00-05696-3

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