Coretractable modules relative to a submodule

Year 2019, Volume: 6 Issue: 2, 95 - 103, 07.05.2019

Ali Reza Moniri Hamzekolaee Yahya Talebi

https://doi.org/10.13069/jacodesmath.561322

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.

Keywords

Coretractable module, N-coretractable module

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