Some Results on Essentially Quasi-DedekindModules

In this paper we give many connections between essentially quasi-Dedekind (quasi-Dedekind) modules and other modules such that Baer modules, retractable modules, essentially retractable modules, compressible modules and essentially compressible modules where an R-module M is called essentially quasi-Dedekind (resp. quasi-Dedekind) if, Hom (M ⁄ N , M )= 0 for all N ≤e M (resp. N ≤ M). Equivalently, a module M is essentially quasi-Dedekind (resp. quasi-Dedekind) if, for each f є End R (M) , Kerf ≤ e M implies f = 0 (resp. f ≠ 0 implies ker f = 0 ).