Geodesic
Modules which have a rad-supplement that is a direct summand in every extension
Algebra and discrete mathematics, Tome 25 (2018) no. 1, pp. 157-164

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In this paper, we introduce the concept of modules with the properties (RE) and (SRE), and we provide various properties of these modules. In particular, we prove that a semisimple module $M$ is $\operatorname{Rad}$-supplementing if and only if $M$ has the property (SRE). Moreover, we show that a ring $R$ is a left V-ring if and only if every left $R$-module with the property (RE) is injective. Finally, we characterize the rings whose modules have the properties (RE) and (SRE).
Keywords: $\operatorname{Rad}$-supplement, module with the properties (RE) and (SRE), artinian serial ring. 
@article{ADM_2018_25_1_a12,
     author = {Burcu Ni\c{s}anc{\i} T\"urkmen and Erg\"ul T\"urkmen},
     title = {Modules which have a rad-supplement that is a direct summand in every extension},
     journal = {Algebra and discrete mathematics},
     pages = {157--164},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_25_1_a12/}
}
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Burcu Nişancı Türkmen; Ergül Türkmen. Modules which have a rad-supplement that is a direct summand in every extension. Algebra and discrete mathematics, Tome 25 (2018) no. 1, pp. 157-164. http://geodesic.mathdoc.fr/item/ADM_2018_25_1_a12/