MMN-4971
On cofinitely (D_{12}^*)-modules
Figen Eryılmaz;Abstract
In this paper, (cofinitely) $\left(D_{12}^*\right)$-modules which are generaliztion of $\oplus_\delta$ - supplemented module are studied. We say that a module $M$ is $\left(D_{12}^*\right)$ - module if for every submodule $A$ of $M$, there exists a direct summand $B$ of $M$ and an epimorphism $f: B \rightarrow \frac{M}{A}$ such that $\operatorname{ker}(f) \ll_\delta B$. The module $M$ is called cofinitely $\left(D_{12}^*\right)$ - module if for every cofinite submodule $A$ of $M$, there exists a direct summand $B$ of $M$ and an epimorphism $f: B \rightarrow \frac{M}{A}$ such that $\operatorname{ker}(f) \ll_\delta B$. In this paper, various properties of these modules are given. In addition, a new characterization of $\delta$-semiperfect rings is given using cofinitely $\left(D_{12}^*\right)-$ modules.
Vol. 26 (2025), No. 2, pp. 757-765