@article { author = {Moniri Hamzekolaee, A. R.}, title = {A GENERALIZATION OF CORETRACTABLE MODULES}, journal = {Journal of Algebraic Systems}, volume = {5}, number = {2}, pages = {163-176}, year = {2018}, publisher = {Shahrood University of Technology}, issn = {2345-5128}, eissn = {2345-511X}, doi = {10.22044/jas.2017.5736.1287}, abstract = {Let $R$ be a ring and $M$ a right $R$-module. We call $M$, coretractable relative to $\overline{Z}(M)$ (for short, $\overline{Z}(M)$-coretractable) provided that, for every proper submodule $N$ of $M$ containing $\overline{Z}(M)$, there is a nonzero homomorphism $f:\dfrac{M}{N}\rightarrow M$. We investigate some conditions under which the two concepts coretractable and $\overline{Z}(M)$-coretractable, coincide. For a commutative semiperfect ring $R$, we show that $R$ is $\overline{Z}(R)$-coretractable if and only if $R$ is a Kasch ring. Some examples are provided to illustrate different concepts.}, keywords = {coretractable module,$overline{Z}(M)$-coretractable module,Kasch ring}, url = {https://jas.shahroodut.ac.ir/article_1100.html}, eprint = {https://jas.shahroodut.ac.ir/article_1100_af402bec4a5048425b463558a46102a6.pdf} }