Geodesic
On generalized CS-modules
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 891-904

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An $\mathscr {S}$-closed submodule of a module $M$ is a submodule $N$ for which $M/N$ is nonsingular. A module $M$ is called a generalized CS-module (or briefly, GCS-module) if any $\mathscr {S}$-closed submodule $N$ of $M$ is a direct summand of $M$. Any homomorphic image of a GCS-module is also a GCS-module. Any direct sum of a singular (uniform) module and a semi-simple module is a GCS-module. All nonsingular right $R$-modules are projective if and only if all right $R$-modules are GCS-modules.
DOI : 10.1007/s10587-015-0215-0
Classification : 16D20, 16D70, 16S99
Keywords: direct summand; $\mathscr {S}$-closed submodule; GCS-module; singular submodule 
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Zeng, Qingyi. On generalized CS-modules. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 891-904. doi: 10.1007/s10587-015-0215-0

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