Manuscripta Mathematica, ( ISI ), Volume (125), Year (2008-5) , Pages (345-352)

Title : ( Asymptotic behaviour of certain sets of associated prime ideals of Ext-modules )

Authors: Fahimeh Khoshahang Ghasr , Kazem Khashyarmanesh ,

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Let R be a commutative Noetherian ring, a be an ideal of R and M be a finitely generated R-module. Melkersson and Schenzel asked whether the set AssRExti R(R/a 6 j , M) 7 becomes stable for a fixed integer i and sufficiently large j . This paper is concerned with this question. In fact, we prove that if s ≥ 0 and n ≥ 0 such that dim(SuppRHi a 8 (M)) ≤ s 9 for all i with i < n, then (i) the set j>0 SuppRExti R R/a j , M≥s 10 is finite for all i with i < n, and (ii) the set j>0 AssRExti R R/a j , M≥s 11 is finite for all i with i ≤ n, 12 where for a subset T of Spec(R), we set (T )≥s := {p ∈ T | dim(R/p) ≥ s}. Also, among other things, we show that if n ≥ 0, R is semi-local and SuppRHi a 13 (M) is finite for all i with i < n, then j>0 AssRExti R(R/a 14 j , M) is finite for all i with i ≤ n.

Keywords

local cohomology
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@article{paperid:1009557,
author = {Khoshahang Ghasr, Fahimeh and Khashyarmanesh, Kazem},
title = {Asymptotic behaviour of certain sets of associated prime ideals of Ext-modules},
journal = {Manuscripta Mathematica},
year = {2008},
volume = {125},
month = {May},
issn = {0025-2611},
pages = {345--352},
numpages = {7},
keywords = {local cohomology modules},
}

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%0 Journal Article
%T Asymptotic behaviour of certain sets of associated prime ideals of Ext-modules
%A Khoshahang Ghasr, Fahimeh
%A Khashyarmanesh, Kazem
%J Manuscripta Mathematica
%@ 0025-2611
%D 2008

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