Dual π-Rickart Modules

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Let R be an arbitrary ring with identity and M a right R-module with S = Endᵣ(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 dual π-Rickart if for any f∈ S, there exist e²=e∈ S and a positive integer n such that Imfⁿ=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.