Small Quasi-Dedekind Modules

Abstract

     Let R be a commutative ring with unity .A unitary R-module M is called    a quasi-Dedekind module if   for all nonzero submodules N of  M .  In this paper we introduce and study the concept of small quasi-Dedekind module as a generalization of quasi-Dedekind module . Where an R-module M is called small quasi-Dedekind if, for each nonzero homomorphisms  f  from M to M , implies Kerf  small in M  ( Kerf  â‰ª M ). And an  R-submodule N of an  R-module M  is called  a small submodule of  M (N ≪ M , for short) if , for  all  K ≤ M  with   N+K = M   implies  K = M