The aim of this paper is to investigate strong notion strongly ⨁-supplemented modules in module theory, namely ⨁-locally artinian supplemented modules. We call a M if it locally and its supplement submodules are direct summand. In study, we provide the basic properties particular, show that every summand supplemented. Moreover, prove ring R semiperfect with radical only projective R-module

We study the class of ADS rings and modules introduced by Fuchs [F]. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that RR is ADS must be either right self-injective or indecomposable as a right Rmodule. Under certain conditions we can construct a unique ADS hull up to isomorphism. We introduce the concept of co...

w x In 8 , K. Morita introduced a useful notion of duality between categories of modules, usually called ‘‘Morita duality.’’ He proved that every duality is given by contravariant hom functors defined by a bimodule which is an injective cogenerator for both categories of modules. On the other hand, the equivalences between categories of comodules over a coalgebra w x were characterized by M. Ta...