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arXiv · 1204.2444

Dual $\pi$-Rickart Modules

Burcu Ungor·Yosum Kurtulmaz·Sait Halıcıoglu·Abdullah Harmanci
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Abstract

Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with $S =$ End$_R(M)$. In this paper we introduce dual $\pi$-Rickart modules as a generalization of $\pi$-regular rings as well as that of dual Rickart modules. The module $M$ is called {\it dual $\pi$-Rickart} if for any $f\in S$, there exist $e^2=e\in S$ and a positive integer $n$ such that Im$f^n=eM$. We prove that some results of dual Rickart modules can be extended to dual $\pi$-Rickart modules for this general settings. We investigate relations between a dual $\pi$-Rickart module and its endomorphism ring.

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Burcu Ungor, Yosum Kurtulmaz, Sait Halıcıoglu, Abdullah Harmanci. 2012-04-11. Dual $\pi$-Rickart Modules. https://arxiv.org/abs/1204.2444

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