On CLS-modules (Q1915738)

Let \(M\) be an \(R\)-module. A submodule \(K\) of \(M\) is defined to be closed if \(M/K\) is non-singular, and \(M\) is a CLS-module if every closed submodule of \(M\) is a direct summand of \(M\). The concept of a CLS-module generalises that of a CS-module, but the concepts coincide for non-singular modules. The direct sum of two CLS-modules need not be a CLS-module. The main result of this paper is that a finite direct sum of relatively injective CLS-modules is a CLS-module.