Asymptotic behavior of associated primes of certain ext modules

Year 2016, Volume: 45 Issue: 5, 1329 - 1334, 01.10.2016

Kamal Bahmanpour Reza Naghipour Mehdi Sehatkhah

Abstract

Let R be a commutative Noetherian ring, I an ideal of R and M a finitely generated R-module. It is shown that, whenever I is principal, then for each integer $i$ the set of associated prime ideals $Ass_R Ext^i_R(R/I^n , M)$, $n = 1, 2, . . . ,$ becomes independent of $n$, for large $n$. 

Keywords

Artinian module, Associated prime, Depth, Noetherian module

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