On $\tau$-extending modules

Talebi, Y., and Mohammadi, R.. "On $\tau $-extending modules." Commentationes Mathematicae Universitatis Carolinae 57.3 (2016): 279-288. <http://eudml.org/doc/286818>.

@article{Talebi2016,
abstract = {In this paper we introduce the concept of $\tau $-extending modules by $\tau $-rational submodules and study some properties of such modules. It is shown that the set of all $\tau $-rational left ideals of $_RR$ is a Gabriel filter. An $R$-module $M$ is called $\tau $-extending if every submodule of $M$ is $\tau $-rational in a direct summand of $M$. It is proved that $M$ is $\tau $-extending if and only if $M = Rej_ME(R/\tau (R))\oplus N$, such that $N$ is a $\tau $-extending submodule of $M$. An example is given to show that the direct sum of $\tau $-extending modules need not be $\tau $-extending.},
author = {Talebi, Y., Mohammadi, R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {torsion theory; $\tau $-rational submodules; $\tau $-closed submodules; $\tau $-extending modules},
language = {eng},
number = {3},
pages = {279-288},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $\tau $-extending modules},
url = {http://eudml.org/doc/286818},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Talebi, Y.
AU - Mohammadi, R.
TI - On $\tau $-extending modules
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 3
SP - 279
EP - 288
AB - In this paper we introduce the concept of $\tau $-extending modules by $\tau $-rational submodules and study some properties of such modules. It is shown that the set of all $\tau $-rational left ideals of $_RR$ is a Gabriel filter. An $R$-module $M$ is called $\tau $-extending if every submodule of $M$ is $\tau $-rational in a direct summand of $M$. It is proved that $M$ is $\tau $-extending if and only if $M = Rej_ME(R/\tau (R))\oplus N$, such that $N$ is a $\tau $-extending submodule of $M$. An example is given to show that the direct sum of $\tau $-extending modules need not be $\tau $-extending.
LA - eng
KW - torsion theory; $\tau $-rational submodules; $\tau $-closed submodules; $\tau $-extending modules
UR - http://eudml.org/doc/286818
ER -