When an S-closed submodule is a direct summand

Abstract

It is well known that a direct sum of CLS-modules is not, in general, a CLS-module. It is proved that if M = M1 ⊕ M2, where M1 and M2 are CLS-modules such that M1 and M2 are relatively ojective (or M1 is M2-ejective), then M is a CLS-module and some known results are generalized. © 2014 Korean Mathematical Society.