On CLS-modules and the S-closure of a submodule

A module M is called a CLS-module if every S-closed submodule of M is a direct summand of M [9]. We give a characterization for CLS-modules and obtain a sufficient condition for CLS-submodules of a CLS-module. Also, we characterize the splitting property in terms of UT-modules and the S-closure of submodules.