On generalized CS-modules

Zeng, Qingyi. "On generalized CS-modules." Czechoslovak Mathematical Journal 65.4 (2015): 891-904. <http://eudml.org/doc/276289>.

@article{Zeng2015,
abstract = {An $\mathcal \{S\}$-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 $\mathcal \{S\}$-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.},
author = {Zeng, Qingyi},
journal = {Czechoslovak Mathematical Journal},
keywords = {direct summand; $\mathcal \{S\}$-closed submodule; GCS-module; singular submodule},
language = {eng},
number = {4},
pages = {891-904},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On generalized CS-modules},
url = {http://eudml.org/doc/276289},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Zeng, Qingyi
TI - On generalized CS-modules
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 4
SP - 891
EP - 904
AB - An $\mathcal {S}$-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 $\mathcal {S}$-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.
LA - eng
KW - direct summand; $\mathcal {S}$-closed submodule; GCS-module; singular submodule
UR - http://eudml.org/doc/276289
ER -