On rings all of whose modules are retractable

Ecevit, Şule, and Koşan, Muhammet Tamer. "On rings all of whose modules are retractable." Archivum Mathematicum 045.1 (2009): 71-74. <http://eudml.org/doc/250684>.

@article{Ecevit2009,
abstract = {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.},
author = {Ecevit, Şule, Koşan, Muhammet Tamer},
journal = {Archivum Mathematicum},
keywords = {retractable module; Morita invariant property; retractable modules; Morita invariants},
language = {eng},
number = {1},
pages = {71-74},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On rings all of whose modules are retractable},
url = {http://eudml.org/doc/250684},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Ecevit, Şule
AU - Koşan, Muhammet Tamer
TI - On rings all of whose modules are retractable
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 1
SP - 71
EP - 74
AB - 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.
LA - eng
KW - retractable module; Morita invariant property; retractable modules; Morita invariants
UR - http://eudml.org/doc/250684
ER -