@article{Amouzegar_2017, title={On K-extending modules}, volume={48}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/1838}, DOI={10.5556/j.tkjm.48.2017.1838}, abstractNote={Let $M$ be a right $R$-module and $S=End_R(M)$. We call $M$ a $\mathcal{K}$-extending module if for every element $\phi\in S$, Ker$\phi$ is essential in a direct summand of $M$. In this paper we investigate these modules. We give a characterization of $\mathcal{K}$-extending modules. We prove that if $M$ is a projective self-generator module, then $M$ is a $\mathcal{K}$-extending module and every finitely generated projective right ideal of $S$ is a summand if and only if $S$ is semiregular and $\Delta(M)=Jac(S)$, where $\Delta(M)=\{f\in S \mid Ker f\leq^e M \}$ if and only if $M$ is $Z(M)$-$\mathcal{I}$-lifting.}, number={1}, journal={Tamkang Journal of Mathematics}, author={Amouzegar, Tayyebeh}, year={2017}, month={Mar.}, pages={1–11} }