strongly duo and co-multiplication modules

Abstract. let r be a commutative ring. an r-module m iscalled co-multiplication, provided that for each submodule n ofm, there exists an ideal i of r such that n = (0 :m i). in thispaper, 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 classesof co-multiplication modules. in addition, if r is a noetherianquasi-injective ring, then r is strongly duo if and only if r isco-multiplication. we also show that j-semisimple strongly duorings are precisely semisimple rings. moreover, if r is a perfectring, then uniserial r-modules are co-multiplication of nite lengthmodules. finally, we show that abelian co-multiplication groupsare all reduced, and co-multiplication z-modules (abelian groups)are characterized as well.