CS Modules Relative to a Torsion Theory

Abstract.

In this article we introduce two new concepts, those of a τ-CS and a s-τ-CS module, which are both torsion-theoretic analogues of CS modules. We investigate their relationship with the familiar concepts of τ-injective, τ-simple and τ-uniform modules and compare them with τ-complemented (τ-injective) modules, which were considered by other authors as torsion-theoretic analogues of CS modules. We are interested in decomposing a relatively CS module into indecomposable submodules, and in determining when a direct sum of relatively CS modules is relatively CS.