On quasi-baer modules

Subject Areas : History and biography

M. Shafiee-Mousavi ¹

1 - Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran

Received: 2016-05-29 Accepted : 2016-08-23 Published : 2016-12-01

Keywords: Quasi-Baer modules, quasi-Armendariz modules, $sigma$-rigid modules,

Abstract :

Let $R$ be a ring, $\sigma$ be an endomorphism of $R$ and $M_R$ be a $\sigma$-rigid module. Amodule $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ isgenerated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if andonly if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,\sigma]]$.

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