TY - JOUR
ID - 728
TI - STRONGLY DUO AND CO-MULTIPLICATION MODULES
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Safaeeyan, S.
AD - Department of Mathematics, University of Yasouj , P.O.Box 75914, Yasouj, IRAN.
Y1 - 2016
PY - 2016
VL - 4
IS - 1
SP - 53
EP - 64
KW - Co-multiplication modules
KW - strongly duo modules
KW - Abelian Groups
DO - 10.22044/jas.2016.728
N2 - 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.
UR - https://jas.shahroodut.ac.ir/article_728.html
L1 - https://jas.shahroodut.ac.ir/article_728_14be7a662ba6a73829b723a3c29433f9.pdf
ER -