A Note on Rickart Modules

2016/09/14 by Ali H. Al-Saedi, Al-Saedi, Ali H., Mehdi S. Abbas +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1609.04113

openalex publication_date 2016/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the notion of Rickart property in a general module theoretic setting as a generalization to the concept of Baer modules and right Rickart rings. A module M_R is called Rickart if the right annihilator in M_R of each left principal ideal of End_R(M) is generated by an idempotent. Characterizations of Rickart modules are given. We give sufficient conditions for direct sums of Rickart modules to be Rickart. We extend some useful results of right Rickart rings to the theory of Rickart modules.

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