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Czechoslovak Mathematical Journal

, Volume 69, Issue 1, pp 225–234 | Cite as

Annihilators of Local Homology Modules

  • Shahram RezaeiEmail author
Article
  • 11 Downloads

Abstract

Let \((R,\mathfrak{m})\) be a local ring, a an ideal of R and M a nonzero Artinian R-module of Noetherian dimension n with hd(a, M) = n. We determine the annihilator of the top local homology module \(H^{\mathfrak{a}}_{n}(M)\). In fact, we prove that
$$\text{Ann}_R(H^{\mathfrak{a}}_{n}(M))=\text{Ann}(N(\mathfrak{a},M)),$$
where \(N(\mathfrak{a},M)\) denotes the smallest submodule of M such that \(\text{hd}(\mathfrak{a},M/N(\mathfrak{a},M))<n\). As a consequence, it follows that for a complete local ring \((R,\mathfrak{m})\) all associated primes of \(H^{\mathfrak{a}}_{n}(M)\) are minimal.

Keywords

local homology Artinian modules annihilator 

MSC 2010

13D45 13E05 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencePayame Noor University (PNU)TehranIran

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