Geodesic
Generalized $\oplus$-supplemented modules
Algebra and discrete mathematics, Tome 10 (2010) no. 2, pp. 10-18

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Let $R$ be a ring and $M$ be a left $R$-module. $M$ is called generalized $\oplus$- supplemented if every submodule of $M$ has a generalized supplement that is a direct summand of $M$. In this paper we give various properties of such modules. We show that any finite direct sum of generalized $\oplus$-supplemented modules is generalized $\oplus$-supplemented. If $M$ is a generalized $\oplus$-supplemented module with $(D3)$, then every direct summand of $M$ is generalized $\oplus$-supplemented. We also give some properties of generalized cover.
Keywords: generalized cover, generalized supplemented module, $\oplus$-supplemented module, generalized $\oplus$-supplemented module. 
@article{ADM_2010_10_2_a1,
     author = {H. \c{C}ali\c{s}ici and E. T\"urkmen},
     title = {Generalized $\oplus$-supplemented modules},
     journal = {Algebra and discrete mathematics},
     pages = {10--18},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2010_10_2_a1/}
}
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H. Çalişici; E. Türkmen. Generalized $\oplus$-supplemented modules. Algebra and discrete mathematics, Tome 10 (2010) no. 2, pp. 10-18. http://geodesic.mathdoc.fr/item/ADM_2010_10_2_a1/