@article{article_561322, title={Coretractable modules relative to a submodule}, journal={Journal of Algebra Combinatorics Discrete Structures and Applications}, volume={6}, pages={95–103}, year={2019}, DOI={10.13069/jacodesmath.561322}, author={Hamzekolaee, Ali Reza Moniri and Talebi, Yahya}, keywords={Coretractable module,N-coretractable module}, abstract={Let $R$ be a ring and $M$ a right $R$-module. Let $N$ be a proper submodule of $M$. We say that $M$ is $N$-coretractable (or $M$ is coretractable relative to $N$) provided that, for every proper submodule $K$ of $M$ containing $N$, there is a nonzero homomorphism $f:M/K\rightarrow M$. We present some conditions that a module $M$ is coretractable if and only if $M$ is coretractable relative to a submodule $N$. We also provide some examples to illustrate special cases.}, number={2}, publisher={iPeak Academy}