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 [۹]. 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.

Keywords:

‎mathscr{S}-closure‎ , ‎CLS-module‎ , ‎splitting property‎