$\tau $-supplemented modules and $\tau $-weakly supplemented modules
Koşan, Muhammet Tamer
Archivum Mathematicum, Tome 043 (2007), p. 251-257 / Harvested from Czech Digital Mathematics Library
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Given a hereditary torsion theory $\tau = (\mathbb {T},\mathbb {F})$ in Mod-$R$, a module $M$ is called $\tau $-supplemented if every submodule $A$ of $M$ contains a direct summand $C$ of $M$ with $A/C$ $\tau -$torsion. A submodule $V$ of $M$ is called $\tau $-supplement of $U$ in $M$ if $U+V=M$ and $U\cap V\le \tau (V)$ and $M$ is $\tau $-weakly supplemented if every submodule of $M$ has a $\tau $-supplement in $M$. Let $M$ be a $\tau $-weakly supplemented module. Then $M$ has a decomposition $M=M_1\oplus M_2$ where $M_1$ is a semisimple module and $M_2$ is a module with $\tau (M_2)\le _e M_2$. Also, it is shown that; any finite sum of $\tau $-weakly supplemented modules is a $\tau $-weakly supplemented module.

Publié le : 2007-01-01
Classification:  16D10,  16D50,  16L60 
@article{108069,
     author = {Muhammet Tamer Ko\c san},
     title = {$\tau $-supplemented modules and $\tau $-weakly supplemented modules},
     journal = {Archivum Mathematicum},
     volume = {043},
     year = {2007},
     pages = {251-257},
     zbl = {1156.16006},
     mrnumber = {2378525},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108069}
}

Koşan, Muhammet Tamer. $\tau $-supplemented modules and $\tau $-weakly supplemented modules. Archivum Mathematicum, Tome 043 (2007) pp. 251-257. http://gdmltest.u-ga.fr/item/108069/

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