Geodesic
On generalized CS-modules
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 891-904
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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 
@article{10_1007_s10587_015_0215_0,
     author = {Zeng, Qingyi},
     title = {On generalized {CS-modules}},
     journal = {Czechoslovak Mathematical Journal},
     pages = {891--904},
     year = {2015},
     volume = {65},
     number = {4},
     doi = {10.1007/s10587-015-0215-0},
     mrnumber = {3441323},
     zbl = {06537698},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0215-0/}
}
TY  - JOUR
AU  - Zeng, Qingyi
TI  - On generalized CS-modules
JO  - Czechoslovak Mathematical Journal
PY  - 2015
SP  - 891
EP  - 904
VL  - 65
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0215-0/
DO  - 10.1007/s10587-015-0215-0
LA  - en
ID  - 10_1007_s10587_015_0215_0
ER  - 
%0 Journal Article
%A Zeng, Qingyi
%T On generalized CS-modules
%J Czechoslovak Mathematical Journal
%D 2015
%P 891-904
%V 65
%N 4
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0215-0/
%R 10.1007/s10587-015-0215-0
%G en
%F 10_1007_s10587_015_0215_0
Zeng, Qingyi. On generalized CS-modules. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 891-904. doi: 10.1007/s10587-015-0215-0

[1] Birkenmeier, G. F., Müller, B. J., Rizvi, S. Tariq: Modules in which every fully invariant submodule is essential in a direct summand. Commun. Algebra 30 (2002), 1395-1415. | DOI | MR

[2] Chatters, A. W., Khuri, S. M.: Endomorphism rings of modules over non-singular CS rings. J. Lond. Math. Soc., II. Ser. 21 (1980), 434-444. | DOI | MR | Zbl

[3] Faith, C.: Algebra. Vol. II: Ring Theory. Grundlehren der Mathematischen Wissenschaften 191 Springer, Berlin (1976), German. | MR | Zbl

[4] Goodearl, K. R.: Ring Theory. Nonsingular Rings and Modules. Pure and Applied Mathematics 33 Marcel Dekker, New York (1976). | MR | Zbl

[5] McAdam, S.: Deep decompositions of modules. Commun. Algebra 26 (1998), 3953-3967. | DOI | MR | Zbl

[6] Nguyen, V. D., Dinh, V. H., Smith, P. F., Wisbauer, R.: Extending Modules. Pitman Research Notes in Mathematics Series 313 Longman Scientific & Technical, Harlow (1994). | MR | Zbl

[7] Wisbauer, R.: Foundations of Module and Ring Theory. Algebra, Logic and Applications 3 Gordon and Breach Science Publishers, Philadelphia (1991). | MR | Zbl

Cité par Sources :