%0 Journal Article
%T STRONGLY DUO AND CO-MULTIPLICATION MODULES
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Safaeeyan, S.
%D 2016
%\ 09/01/2016
%V 4
%N 1
%P 53-64
%! STRONGLY DUO AND CO-MULTIPLICATION MODULES
%K Co-multiplication modules
%K strongly duo modules
%K Abelian Groups
%R 10.22044/jas.2016.728
%X Let R be a commutative ring. An R-module M is called co-multiplication provided that foreach submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper weshow that co-multiplication modules are a generalization of strongly duo modules. Uniserialmodules of finite length and hence valuation Artinian rings are some distinguished classes ofco-multiplication rings. In addition, if R is a Noetherian ring, then R is a strongly duoring if and only if R is a co-multiplication ring. We also show that J-semisimple strongly duorings are precisely semisimple rings. Moreover, if R is a perfect ring, then uniserial R-modules are co-multiplication of finite length modules. Finally, we showthat Abelian co-multiplication groups are reduced and co-multiplication Z-modules(Abeliangroups)are characterized.
%U https://jas.shahroodut.ac.ir/article_728_14be7a662ba6a73829b723a3c29433f9.pdf