Some Characterizations of $I$-modules

Mankagna Albert Diompy, Oumar Diankha, Mamadou Sanghare

Abstract


Let $R$ be a non-necessarily commutative ring and $M$ an $R$-module. We use the category $\sigma[M]$ to introduce the notion of $I$-module who is a generalization of $I$-ring. It is well known that every artinian object of $\sigma [M]$ is co-hopfian but the converse is not true in general.

The aim of this paper is to characterize for a fixed ring, the left (right) $R$-modules $M$ for which every co-hopfian object of $\sigma[M]$ is artinian.

We obtain some characterization of finitely generated $I$-modules  over a commutative ring, faithfully balanced finitely generated $I$-modules, and left serial finitely generated $I$-modules over a duo-ring.

Full Text: PDF DOI: 10.5539/jmr.v4n6p106

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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