ESSENTIALLY SEMIMALL QUASI-DEDEKIND MODULES AND ANTI-HOPFIAN MODULES

Abstract

Let V be a ring with identity and S be a unitary left Module over V. An 𝐑-Module S is essentially semismall quasi-Dedekind (ESSQD) whether Hom(S/H,S) = 0 H es S. A ring V is ESSQD if V is an ESSQD V-Module. An V -Module S is anti-hopfian if S is nonsimple and all nonzero factor Modules of S are isomorphic to S; that is for all , S Y  S . In this paper we study the relationship between ESSQD with anti-hopfian Modules and continuous Modules. We also give some examples to illustrate these relationships.