Abstract
Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules.
 The main purpose of this paper is to develop the properties of Rickart modules .
 We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules.
Highlights
A module is called a Rickart module if for every, for some .Equivalently a module is a Rickart module if and only if for every is a direct summand of, See [1], [2] .In this paper, we give some results on the Rickart modules
We give some results on the Rickart modules
We study the direct sum of Rickart modules
Summary
A module is a Rickart module if and only if for every is a direct summand of , See [1], [2]. We give some results on the Rickart modules. We study the direct sum of Rickart modules. For example we prove that an -module is Rickart if and only if. For example we prove that a ring is semisimple if and only if all injective -module is Rickart , see Theorem (3.12). Throughout this article, is a ring with identity and is a unital left -module. The notations mean that is a submodule, a direct summand of
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