On $FGDF$-modules

Alhousseynou Ba, Sidy Demba Tour\'e and Oumar Diankha

Journal of Mathematics Research, 2017, vol. 9, issue 4, 196-199

Abstract: Let $R$ be a unital ring and $M$ a unitary module not necessary over $R$. The $FGDF$-module is a generalization of $FGDF$-rings (Tour\'e, Diop, Mohamed and Sanghar\'e, 2014). In this work, we first give some properties of $FGDF$-modules. After that, we show that for a finitely generated module $M$, $M$ is a $FGDF$-module if and only if $M$ is of finite representation type module. Finally, we show that $M$ is a finitely generated $FGDF$-module if and only if every Dedekind finite module of $\sigma[M]$ is noetherian.

Keywords: finitely generated module; Dedekind finite module; $FGDF$-module (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:196-199

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