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arXiv · 2005.02059

A new approach to Baer and dual Baer modules

N. Ghaedan·M. R. Vedadi
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Abstract

Let $R$ be a ring. It is proved that an $R$-module $M$ is Baer (resp. dual Baer) if and only if every exact sequence $0\rightarrow X\rightarrow M\rightarrow Y\rightarrow 0$ with $Y\in$ Cog$(M_R)$ (resp. $X\in$ Gen$(M_R)$) splits. This shows that being (dual) Baer is a Morita invariant property. As more applications, the Baer condition for the $R$-module $M^+ $ = Hom$_{\Bbb Z}(M,{\Bbb Q}/{\Bbb Z})$ is investigated and shown that $R$ is a von Neumann regular ring, if $R^+$ is a Baer $R$-module. Baer modules with (weak) chain conditions are studied and determined when a Baer (resp. dual baer) module is a direct sum of mutually orthogonal prime (resp. co-prime) modules. Finitely generated dual Baer modules over commutative rings are studeid

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N. Ghaedan, M. R. Vedadi. 2020-05-05. A new approach to Baer and dual Baer modules. https://arxiv.org/abs/2005.02059

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