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retractable module; Morita invariant property
Let $R$ be a ring. A right $R$-module $M$ is said to be retractable if $\mathbb{T}{Hom}_R(M,N)\ne 0$ whenever $N$ is a non-zero submodule of $M$. The goal of this article is to investigate a ring $R$ for which every right R-module is retractable. Such a ring will be called right mod-retractable. We proved that $(1)$ The ring $\prod _{i \in \mathcal{I}} R_i$ is right mod-retractable if and only if each $R_i$ is a right mod-retractable ring for each $i\in \mathcal{I}$, where $\mathcal{I}$ is an arbitrary finite set. $(2)$ If $R[x]$ is a mod-retractable ring then $R$ is a mod-retractable ring.
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