Geodesic
Modules whose maximal submodules have $\tau$-supplements
Algebra and discrete mathematics, Tome 10 (2010) no. 2, pp. 1-9.

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Let $R$ be a ring and $\tau$ be a preradical for the category of left $R$-modules. In this paper, we study on modules whose maximal submodules have $\tau$-supplements. We give some characterizations of these modules in terms their certain submodules, so called $\tau$-local submodules. For some certain preradicals $\tau$, i.e. $\tau=\delta$ and idempotent $\tau$, we prove that every maximal submodule of $M$ has a $\tau$-supplement if and only if every cofinite submodule of $M$ has a $\tau$-supplement. For a radical $\tau$ on R-Mod, we prove that, for every $R$-module every submodule is a $\tau$-supplement if and only if $R/\tau(R)$ is semisimple and $\tau$ is hereditary.
Keywords: preradical, $\tau$-supplement, $\tau$-local. 
@article{ADM_2010_10_2_a0,
     author = {E. B\"uy\"uka\c{s}ik},
     title = {Modules whose maximal submodules have $\tau$-supplements},
     journal = {Algebra and discrete mathematics},
     pages = {1--9},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2010_10_2_a0/}
}
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E. Büyükaşik. Modules whose maximal submodules have $\tau$-supplements. Algebra and discrete mathematics, Tome 10 (2010) no. 2, pp. 1-9. http://geodesic.mathdoc.fr/item/ADM_2010_10_2_a0/