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Moharram Aghapournahr

Moharram Aghapournahr

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-8265-9700
Education: PhD.
ScopusId: 24179345700
Faculty: Science
Address: Arak University
Phone:

Research

Title
A Note on Cofinite Modules
Type
JournalPaper
Keywords
Arithmetic rank; Cofinite modules; Local cohomology
Year
2016
Journal Communications in Algebra
DOI
Researchers Moharram Aghapournahr ، KAMAL BAHMANPOUR

Abstract

Let R be a commutative Noetherian ring, I an ideal of R, and M an arbitrary R-module. It is shown that the R-module Exti RR/I M is finitely generated, for all i ≥ 0, if and only if the R-module Exti RR/I M is finitely generated, for all 0 ≤ i ≤ araI. As an immediate consequence, we prove that, if R is a Noetherian (resp. R is a Noetherian local) ring of dimension d, then the R-module Exti RR/I M is finitely generated, for all i ≥ 0 if and only if the R-module Exti RR/I M is finitely generated, for all 0 ≤ i ≤ d + 1 (resp. for all 0 ≤ i ≤ d). Also, it is shown that, if I = Rx1 +· · ·+Rxn n ≥ 1 and SuppRM ⊆ VI, then M is I-cofinite if and only if the R-module Exti RR/I M or TorRi R/I M is finitely generated, for all 0 ≤ i ≤ n.