Geodesic
On Generalization of Injective Modules
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 249

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As a proper generalization of injective modules in term of supplements, we say that a module $M$ has \emph{the property} (SE) (respectively, \emph{the property} (SSE)) if, whenever $M\subseteq N$, $M$ has a supplement that is a direct summand of $N$ (respectively, a strong supplement in $N$). We show that a ring $R$ is a left and right artinian serial ring with $\operatorname{Rad}(R)^2=0$ if and only if every left $R$-module has the property (SSE). We prove that a commutative ring $R$ is an artinian serial ring if and only if every left $R$-module has the property~(SE).
DOI : 10.2298/PIM141215014T
Classification : 16D10 16D50
Keywords: supplement, module with the properties (SE) and (SSE), artinian serial ring 
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     title = {On {Generalization} of {Injective} {Modules}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {249 },
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Burcu Nişancı Türkmen. On Generalization of Injective Modules. Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 249 . doi: 10.2298/PIM141215014T

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