Geodesic
Amply (weakly) Goldie-Rad-supplemented~modules
Algebra and discrete mathematics, Tome 22 (2016) no. 1, pp. 94-101.

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Let $R$ be a ring and $M$ be a right $R$-module. We say a submodule $S$ of $M$ is a (weak) Goldie-Rad-supplement of a submodule $N$ in $M$, if $M=N+S$, $(N\cap S \leq Rad(M))$ $N\cap S\leq Rad(S)$ and $N\beta^{**} S$, and $M$ is called amply (weakly) Goldie-Rad-supplemented if every submodule of $M$ has ample (weak) Goldie-Rad-supplements in $M$. In this paper we study various properties of such modules. We show that every distributive projective weakly Goldie-Rad-Supplemented module is amply weakly Goldie-Rad-Supplemented. We also show that if $M$ is amply (weakly) Goldie-Rad-supplemented and satisfies DCC on (weak) Goldie-Rad-supplement submodules and on small submodules, then $M$ is Artinian.
Keywords: supplement submodule, Goldie-Rad-Supplement submodule, amply Goldie-Rad-Supplemented module. 
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     author = {Figen Tak{\i}l Mutlu},
     title = {Amply (weakly) {Goldie-Rad-supplemented~modules}},
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     volume = {22},
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     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a5/}
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Figen Takıl Mutlu. Amply (weakly) Goldie-Rad-supplemented~modules. Algebra and discrete mathematics, Tome 22 (2016) no. 1, pp. 94-101. http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a5/

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