Geodesic
On $\tau$-extending modules
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 3, pp. 279-288.

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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.
DOI : 10.14712/1213-7243.2015.172
Classification : 16D10, 16D80, 16D99
Keywords: torsion theory; $\tau$-rational submodules; $\tau$-closed submodules; $\tau$-extending modules 
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Talebi, Y.; Mohammadi, R. On $\tau$-extending modules. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 3, pp. 279-288. doi : 10.14712/1213-7243.2015.172. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.172/

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