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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A dimension inequality for Cohen-Macaulay rings


Author: Sean Sather-Wagstaff
Journal: Trans. Amer. Math. Soc. 354 (2002), 993-1005
MSC (2000): Primary 13H15, 13C15; Secondary 13H05, 13D22
Published electronically: August 21, 2001
MathSciNet review: 1867369
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Abstract: The recent work of Kurano and Roberts on Serre's positivity conjecture suggests the following dimension inequality: for prime ideals $\mathfrak{p}$ and $\mathfrak{q}$ in a local, Cohen-Macaulay ring $(A,\mathfrak{n})$ such that $e(A_{\mathfrak{p}})=e(A)$ we have $\dim(A/\mathfrak{p})+\dim(A/\mathfrak{q})\leq\dim(A)$. We establish this dimension inequality for excellent, local, Cohen-Macaulay rings which contain a field, for certain low-dimensional cases and when $R/\mathfrak{p}$ is regular.


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Additional Information

Sean Sather-Wagstaff
Affiliation: Department of Mathematics, University of Utah, 155 S. 1400 E., Salt Lake City, Utah 84112-0090
Address at time of publication: Department of Mathematics, University of Illinois, 273 Altgeld Hall, 1409 W. Green St., Urbana, Illinois 61801
Email: ssather@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02870-7
PII: S 0002-9947(01)02870-7
Keywords: Intersection dimension, intersection multiplicities, multiplicities
Received by editor(s): December 20, 1999
Received by editor(s) in revised form: March 1, 2000
Published electronically: August 21, 2001
Article copyright: © Copyright 2001 American Mathematical Society