- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 2
- On a generalization of $C_2$-modules
On a generalization of $C_2$-modules
Authors : Abdoul Djibril Diallo, Papa Cheikhou Diop, Rachid Tribak
Pages : 430-442
Doi:10.15672/hujms.792212
View : 14 | Download : 5
Publication Date : 2022-04-01
Article Type : Research
Abstract :A module $M$ is called a $C_{21}$-module if, whenever $A$ and $B$ are submodules of $M$ with $A \cong B$, $A$ is nonsingular and $B$ is a direct summand of $M$, then $A$ is a direct summand of $M$. Various examples of $C_{21}$-modules are presented. Some basic properties of these modules are investigated. It is shown that the class of rings $R$ over which every $C_{21}$-module is a $C_2$-module is exactly that of right SI-rings. Also, we prove that for a ring $R$, every $R$-module has $(C_{21})$ if and only if $R$ is a right t-semisimple ring.Keywords : $C_{21}$-module, $C_2$-module, nonsingular module, singular module, SI-ring, t-semisimple ring