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

Published electronically:
October 25, 2000

MathSciNet review:
1814157

Full-text PDF Free Access

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.

**1.**Ian M. Aberbach and Craig Huneke,*An improved Briançon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras*, Math. Ann.**297**(1993), no. 2, 343–369. MR**1241812**, 10.1007/BF01459507**2.**M. Chardin, D. Eisenbud and B. Ulrich, Hilbert functions, residual intersections, and residually ideals, Compositio Math., to appear.**3.**Alberto Corso, Craig Huneke, and Wolmer V. Vasconcelos,*On the integral closure of ideals*, Manuscripta Math.**95**(1998), no. 3, 331–347. MR**1612078**, 10.1007/s002290050033**4.**A. Corso, C. Polini and B. Ulrich, Core of ideals and modules with the expected reduction number, preprint 2000.**5.**C. Huneke, A cancellation theorem for ideals, J. Pure & Applied Algebra, to appear.**6.**Mark Johnson and Bernd Ulrich,*Artin-Nagata properties and Cohen-Macaulay associated graded rings*, Compositio Math.**103**(1996), no. 1, 7–29. MR**1404996****7.**Joseph Lipman and Avinash Sathaye,*Jacobian ideals and a theorem of Briançon-Skoda*, Michigan Math. J.**28**(1981), no. 2, 199–222. MR**616270****8.**Claudia Polini and Bernd Ulrich,*Linkage and reduction numbers*, Math. Ann.**310**(1998), no. 4, 631–651. MR**1619911**, 10.1007/s002080050163**9.**C. Polini and B. Ulrich, Necessary and sufficient conditions for the Cohen-Macaulayness of blowup algebras, Compositio Math.**119**(1999), 185-207. CMP**2000:04****10.**A. Simis, B. Ulrich and W.V. Vasconcelos, Rees algebras of modules, preprint 1998.**11.**Bernd Ulrich,*Artin-Nagata properties and reductions of ideals*, Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992) Contemp. Math., vol. 159, Amer. Math. Soc., Providence, RI, 1994, pp. 373–400. MR**1266194**, 10.1090/conm/159/01519**12.**Bernd Ulrich,*Ideals having the expected reduction number*, Amer. J. Math.**118**(1996), no. 1, 17–38. MR**1375302**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
13A30,
13B22,
13C10,
13C40

Retrieve articles in all journals with MSC (2000): 13A30, 13B22, 13C10, 13C40

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