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

 

What is a system of parameters?


Authors: Louiza Fouli and Craig Huneke
Journal: Proc. Amer. Math. Soc. 139 (2011), 2681-2696
MSC (2010): Primary 13A35, 13C40, 13D45
Published electronically: February 8, 2011
MathSciNet review: 2801607
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Abstract: In this paper we discuss various refinements and generalizations of a theorem of Sankar Dutta and Paul Roberts. Their theorem gives a criterion for $ d$ elements in a $ d$-dimensional Noetherian Cohen-Macaulay local ring to be a system of parameters, i.e., to have height $ d$. We chiefly remove the assumption that the ring be Cohen-Macaulay and discuss similar theorems.


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Additional Information

Louiza Fouli
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
Email: lfouli@math.nmsu.edu

Craig Huneke
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: huneke@math.ku.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10790-1
PII: S 0002-9939(2011)10790-1
Keywords: System of parameters, local cohomology, limit closure, tight closure, plus closure
Received by editor(s): March 15, 2010
Received by editor(s) in revised form: August 2, 2010
Published electronically: February 8, 2011
Additional Notes: The first author was partially supported by the NSF-AWM Mentoring Travel Grant, grant DMS-0839954. She thanks the Department of Mathematics at the University of Kansas for its hospitality.
The second author was partially supported by the National Science Foundation, grant DMS-0756853.
Communicated by: Irena Peeva
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.