Geodesic
On rings all of whose modules are retractable
Archivum mathematicum, Tome 45 (2009) no. 1, pp. 71-74

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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.
Classification : 16D10, 16D50, 16D70, 16D80, 16D90, 16S36
Keywords: retractable module; Morita invariant property 
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     author = {Ecevit, \c{S}ule and Ko\c{s}an, Muhammet Tamer},
     title = {On rings all of whose modules are retractable},
     journal = {Archivum mathematicum},
     pages = {71--74},
     publisher = {mathdoc},
     volume = {45},
     number = {1},
     year = {2009},
     mrnumber = {2591662},
     zbl = {1203.16006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2009__45_1_a5/}
}
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Ecevit, Şule; Koşan, Muhammet Tamer. On rings all of whose modules are retractable. Archivum mathematicum, Tome 45 (2009) no. 1, pp. 71-74. http://geodesic.mathdoc.fr/item/ARM_2009__45_1_a5/