H-cofinitely supplemented modules and their Properties

Let M be a module. A submodule N of M is called cofinite in M if the factor module M/N is finitely generated. A module M is called H-cofinitely supplemented if for every cofinite submodule E of M there exists a direct summand D of M such that M = E+X holds if and only if M = D+X, for all X ⩽ M. In this paper we study H-cofinitely supplemented modules and obtain some related results