STRONGLY DUO AND CO-MULTIPLICATION MODULES

Abstract. 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 :M I). In this paper, we show that co-multiplication modules are a generaliza- tion of strongly duo modules. Uniserial modules of nite length, and hence, valuation Artinian rings are some distinguished classes of co-multiplication modules. In addition, if R is a Noetherian quasi-injective ring, then R is strongly duo if and only if R is co-multiplication. 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 nite length modules. Finally, we show that Abelian co-multiplication groups are all reduced, and co-multiplication Z-modules (Abelian groups) are characterized as well.