STRONGLY DUO AND CO-MULTIPLICATION MODULES

Let R be a commutative ring. An R-module M is called co-multiplication provided that for each submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper we show that co-multiplication modules are a generalization of strongly duo modules. Uniserial modules of finite length and hence valuation Artinian rings are some distinguished classes of co-multiplication rings. In addition, if R is a Noetherian ring, then R is a strongly duo ring if and only if R is a co-multiplication ring. We also show that J-semisimple strongly duo rings are precisely semisimple rings. Moreover, if R is a perfect ring, then uniserial R modules are co-multiplication of finite length modules. Finally, we show that Abelian co-multiplication groups are reduced and co-multiplication Z-modules(Abelian groups)are characterized.