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Dual $π$-Rickart Modules

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 $π$-Rickart modules as a generalization of $π$-regular rings as well as that of dual Rickart modules. The module $M$ is called {\it dual $π$-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 $π$-Rickart modules for this general settings. We investigate relations between a dual $π$-Rickart module and its endomorphism ring.