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Title: On generalized CS-modules (English)
Author: Zeng, Qingyi
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 65
Issue: 4
Year: 2015
Pages: 891-904
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: direct summand
Keyword: $\mathscr {S}$-closed submodule
Keyword: GCS-module
Keyword: singular submodule
MSC: 16D20
MSC: 16D70
MSC: 16S99
idZBL: Zbl 06537698
idMR: MR3441323
DOI: 10.1007/s10587-015-0215-0
Date available: 2016-01-13T09:02:08Z
Last updated: 2020-07-03
Stable URL:
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