A dimension inequality for Cohen-Macaulay rings

Citation
S. Sather-wagstaff, A dimension inequality for Cohen-Macaulay rings, T AM MATH S, 354(3), 2002, pp. 993-1005
Citations number
13
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
0002-9947 → ACNP
Volume
354
Issue
3
Year of publication
2002
Pages
993 - 1005
Database
ISI
SICI code
0002-9947(2002)354:3<993:ADIFCR>2.0.ZU;2-N
Abstract
The recent work of Kurano and Roberts on Serre's positivity conjecture sugg ests the following dimension inequality: for prime ideals p and q in a loca l, Cohen-Macaulay ring (A, n) such that e(A(p)) = e(A) we have dim(A/p) +di m(A/q) less than or equal to dim(A). We establish this dimension inequality for excellent, local, Cohen-Macaulay rings which contain a field, for cert ain low-dimensional cases and when R/p is regular.