Document Type: Original Manuscript

Author

Department of Mathematics, University of Yasouj , P.O.Box 75914, Yasouj, IRAN.

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 : 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.

Keywords