Weakly Secondary Submodules

Abstract

Let  be a non-zero right module over a ring  with an identity. The weakly secondary submodule is introduced in this paper. A non-zero submodule  of   is weakly secondary submodule when  ,  where ,  and  is a submodule of  implies either  or   for some positive integer . Some relationships between this class of modules and other related modules are discussed and number of conclusions and characterizations are obtained.