MODULES WHOSE EC-CLOSED SUBMODULES ARE DIRECT SUMMAND

Abstract

A module $M$ is called ECS if every ec-closed submodule of $M$ is a direct summand. It was shown that the ECS property lies strictly between CS and P-extending properties. We studied modules $M$ such that every homomorphism from an ec-closed submodule of $M$ to $M$ can be lifted to $M$. Although such modules share some of the properties of ECS-modules, it is shown that they form a substantially bigger class of modules.