On $\mu$-singular and $\mu$-extending modules

Talebi, Yahya, and Hamzekolaee, Ali Reza Moniri. "On $\mu $-singular and $\mu $-extending modules." Archivum Mathematicum 048.3 (2012): 183-196. <http://eudml.org/doc/246507>.

@article{Talebi2012,
abstract = {Let $M$ be a module and $\mu $ be a class of modules in $\operatorname\{Mod\}-R$ which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defines a $\mu $-essential submodule provided it has a non-zero intersection with any non-zero submodule in $\mu $. We define and investigate $\mu $-singular modules. We also introduce $\mu $-extending and weakly $\mu $-extending modules and mainly study weakly $\mu $-extending modules. We give some characterizations of $\mu $-co-H-rings by weakly $\mu $-extending modules. Let $R$ be a right non-$\mu $-singular ring such that all injective modules are non-$\mu $-singular, then $R$ is right $\mu $-co-H-ring if and only if $R$ is a QF-ring.},
author = {Talebi, Yahya, Hamzekolaee, Ali Reza Moniri},
journal = {Archivum Mathematicum},
keywords = {$\mu $-essential submodule; $\mu $-singular module; $\mu $-extending module; weakly $\mu $-extending module; essential submodules; singular modules; -extending modules; weakly extending modules},
language = {eng},
number = {3},
pages = {183-196},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On $\mu $-singular and $\mu $-extending modules},
url = {http://eudml.org/doc/246507},
volume = {048},
year = {2012},
}

TY - JOUR
AU - Talebi, Yahya
AU - Hamzekolaee, Ali Reza Moniri
TI - On $\mu $-singular and $\mu $-extending modules
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 3
SP - 183
EP - 196
AB - Let $M$ be a module and $\mu $ be a class of modules in $\operatorname{Mod}-R$ which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defines a $\mu $-essential submodule provided it has a non-zero intersection with any non-zero submodule in $\mu $. We define and investigate $\mu $-singular modules. We also introduce $\mu $-extending and weakly $\mu $-extending modules and mainly study weakly $\mu $-extending modules. We give some characterizations of $\mu $-co-H-rings by weakly $\mu $-extending modules. Let $R$ be a right non-$\mu $-singular ring such that all injective modules are non-$\mu $-singular, then $R$ is right $\mu $-co-H-ring if and only if $R$ is a QF-ring.
LA - eng
KW - $\mu $-essential submodule; $\mu $-singular module; $\mu $-extending module; weakly $\mu $-extending module; essential submodules; singular modules; -extending modules; weakly extending modules
UR - http://eudml.org/doc/246507
ER -