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In this paper, we provide the basic properties of (semi)simple hypermodules. We show that if a hypermodule M is simple, then (End(M), ·) is a group, where End(M) is the set of all normal endomorphisms of M. We prove that every simple hypermodule is normal projective with a zero singular subhypermodu ...

In this work, we introduce ps-supplement submodules as a kind of supplements. Specifically, a submodule V of a module M is referred to as a ps-supplement if there exists another submodule U⊆M such that M=U+V and the intersection U∩V is projective semisimple. We demonstrate that, over an arbitrary ri ...

Recently, the concept of subprojectivity domains for modules has been introduced as a means of quantifying the level of projectivity exhibited by a module. In this research article, we focus on the subprojectivity domain of Goldie torsion modules. In particular, we establish that a ring denoted as R ...