Modules whose ec-closed submodules are direct summand. (Q730659)

Let \(N\) be a submodule of \(M\). If \(N\) is a closed submodule of \(M\) and \(N\) contains essentially a cyclic submodule, then \(N\) is called an ec-closed submodule of \(M\). If every ec-closed submodule of \(M\) is a direct summand, then \(M\) is called an ECS-module. ECS property lies strictly between CS and P-extending properties. In this paper the authors study 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.