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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
Abelian Category of Cominimax and Weakly Cofi nite Modules
Type
JournalPaper
Keywords
Co nite modules, Cominimax modules,Weakly co nite modules, Abelian category, Arithmetic rank.
Year
2016
Journal TAIWAN J MATH
DOI
Researchers Moharram Aghapournahr

Abstract

Let R be a commutative Noetherian ring, I an ideal of R and M an arbitrary R-module. Let S be a Serre subcategory of the category of R-modules. It is shown that the R-module Exti R(R=I;M) belongs to S, for all i  0, if and only if the R-module Exti R(R=I;M) belongs to S, for all 0  i  ara(I). As an immediate consequence, we prove that if R is a Noetherian (resp. (R;m) is a Noetherian local) ring of dimension d, then the R-module Exti R(R=I;M) belongs to S, for all i  0 if and only if the R-module Exti R(R=I;M) belongs to S, for all 0  i  d+1 (resp. for all 0  i  d). Also it is shown that if I is a principal ideal up to radical, then the category of I-cominimax (resp. I-weakly co nite) modules is an Abelian full subcategory of the category of R-modules.