Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
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

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.


References [Enhancements On Off] (What's this?)

  • 1. I. M. Aberbach and C. Huneke, An improved Briançon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras, Math. Ann. 297 (1993), 343-369. MR 95b:13005
  • 2. M. Chardin, D. Eisenbud and B. Ulrich, Hilbert functions, residual intersections, and residually $S_2$ ideals, Compositio Math., to appear.
  • 3. A. Corso, C. Huneke and W.V. Vasconcelos, On the integral closure of ideals, Manuscripta Math. 95 (1998), 331-347. MR 99b:13010
  • 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. M. Johnson and B. Ulrich, Artin-Nagata properties and Cohen-Macaulay associated graded rings, Compositio Math. 103 (1996), 7-29. MR 97f:13006
  • 7. J. Lipman and A. Sathaye, Jacobian ideals and a theorem of Briançon-Skoda, Michigan Math. J. 28 (1981), 97-116. MR 83m:13001
  • 8. C. Polini and B. Ulrich, Linkage and reduction numbers, Math. Ann. 310 (1998), 631-651. MR 99g:13017
  • 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. B. Ulrich, Artin-Nagata properties and reductions of ideals, in Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, W. Heinzer, C. Huneke, J. Sally (eds.), Contemp. Math. 159, Amer. Math. Soc., Providence, 1994, 373-400. MR 95a:13017
  • 12. B. Ulrich, Ideals having the expected reduction number, Amer. J. Math. 118 (1996), 17-38. MR 97b:13003

Similar Articles

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

American Mathematical Society