On generalized CS-modules |
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Authors: | Qingyi Zeng |
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Affiliation: | 1. Department of Mathematics, Shaoguan University, Daxue Road No. 288, Zhenjiang, Shaoguan, 512005, Guangdong, China
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Abstract: | An 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 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. |
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