Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584544 | Journal of Algebra | 2014 | 11 Pages |
Abstract
Let (R,m) be a Noetherian local ring and M a finitely generated R-module. Following I.G. Macdonald [8], the set of all attached primes of the Artinian local cohomology module Hmi(M) is denoted by AttR(Hmi(M)). In [13, Theorem 3.7], R.Y. Sharp proved that if R is a quotient of a Gorenstein local ring then the shifted localization principle holds true for any local cohomology modules Hmi(M), i.e.(1)AttRp(HpRpiâdimâ¡(R/p)(Mp))={qRp|qâAttRHmi(M),qâp} for any pâSpec(R). In this paper, we improve Sharp's result as follows: the shifted localization principle holds true if and only if R is universally catenary and all its formal fibers are Cohen-Macaulay, if and only if the shifted completion principle(2)AttRË(Hmi(M))=âpâAttR(Hmi(M))AssRË(RË/pRË) holds true for any local cohomology module Hmi(M). This also improves the main result of the paper by T.D.M. Chau and the first author [2].
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Le Thanh Nhan, Pham Hung Quy,