| 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:
|
http://hdl.handle.net/10338.dmlcz/144780 |
| . |
| Reference:
|
[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. MR 1892606, 10.1080/00927870209342387 |
| Reference:
|
[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. Zbl 0432.16017, MR 0577719, 10.1112/jlms/s2-21.3.434 |
| Reference:
|
[3] Faith, C.: Algebra. Vol. II: Ring Theory.Grundlehren der Mathematischen Wissenschaften 191 Springer, Berlin (1976), German. Zbl 0335.16002, MR 0427349 |
| Reference:
|
[4] Goodearl, K. R.: Ring Theory. Nonsingular Rings and Modules.Pure and Applied Mathematics 33 Marcel Dekker, New York (1976). Zbl 0336.16001, MR 0429962 |
| Reference:
|
[5] McAdam, S.: Deep decompositions of modules.Commun. Algebra 26 (1998), 3953-3967. Zbl 0937.13003, MR 1661248, 10.1080/00927879808826387 |
| Reference:
|
[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). Zbl 0841.16001, MR 1312366 |
| Reference:
|
[7] Wisbauer, R.: Foundations of Module and Ring Theory.Algebra, Logic and Applications 3 Gordon and Breach Science Publishers, Philadelphia (1991). Zbl 0746.16001, MR 1144522 |
| . |
