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

 

Serre's condition $R_{k}$ for associated graded rings


Authors: Mark Johnson and Bernd Ulrich
Journal: Proc. Amer. Math. Soc. 127 (1999), 2619-2624
MSC (1991): Primary 13A30; Secondary 13H10
Published electronically: April 23, 1999
MathSciNet review: 1600093
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Abstract: A criterion is given for when the associated graded ring of an ideal satisfies Serre's condition $R_{k}$. As an application, the integrality and quasi-Gorensteinness of such rings is investigated.


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Additional Information

Mark Johnson
Affiliation: Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701
Email: mark@math.uark.edu

Bernd Ulrich
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: ulrich@math.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04841-8
PII: S 0002-9939(99)04841-8
Received by editor(s): September 15, 1997
Received by editor(s) in revised form: December 1, 1997
Published electronically: April 23, 1999
Additional Notes: The second author was partially supported by the NSF
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society