Geodesic
$F$-supplemented modules
Algebra and discrete mathematics, Tome 30 (2020) no. 1, pp. 83-96

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Let $R$ be a ring, let $M$ be a left $R$-module, and let $U, V, F$ be submodules of $M$ with $F$ proper. We call $V$ an $F$-supplement of $U$ in $M$ if $V$ is minimal in the set $ F \subseteq X \subseteq M$ such that $U + X = M$, or equivalently, $F\subseteq V$, $U + V = M$ and $U \cap V$ is $F$-small in $V$. If every submodule of $M$ has an $F$-supplement, then we call $M$ an $F$-supplemented module. In this paper, we introduce and investigate $F$-supplement submodules and (amply) $F$-supplemented modules. We give some properties of these modules, and characterize finitely generated (amply) $F$-supplemented modules in terms of their certain submodules.
Keywords: $F$-supplement and $F$-small submodules, $F$-supplemented, $F$-local and $F$-hollow modules. 
@article{ADM_2020_30_1_a7,
     author = {S. \"Ozdemir},
     title = {$F$-supplemented modules},
     journal = {Algebra and discrete mathematics},
     pages = {83--96},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_30_1_a7/}
}
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S. Özdemir. $F$-supplemented modules. Algebra and discrete mathematics, Tome 30 (2020) no. 1, pp. 83-96. http://geodesic.mathdoc.fr/item/ADM_2020_30_1_a7/