| Title:
|
On rings all of whose modules are retractable (English) |
| Author:
|
Ecevit, Şule |
| Author:
|
Koşan, Muhammet Tamer |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
71-74 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a ring. A right $R$-module $M$ is said to be retractable if $\mathbb{T}{Hom}_R(M,N)\ne 0$ whenever $N$ is a non-zero submodule of $M$. The goal of this article is to investigate a ring $R$ for which every right R-module is retractable. Such a ring will be called right mod-retractable. We proved that
$(1)$ The ring $\prod _{i \in \mathcal{I}} R_i$ is right mod-retractable if and only if each $R_i$ is a right mod-retractable ring for each $i\in \mathcal{I}$, where $\mathcal{I}$ is an arbitrary finite set.
$(2)$ If $R[x]$ is a mod-retractable ring then $R$ is a mod-retractable ring. (English) |
| Keyword:
|
retractable module |
| Keyword:
|
Morita invariant property |
| MSC:
|
16D10 |
| MSC:
|
16D50 |
| MSC:
|
16D70 |
| MSC:
|
16D80 |
| MSC:
|
16D90 |
| MSC:
|
16S36 |
| idZBL:
|
Zbl 1203.16006 |
| idMR:
|
MR2591662 |
| . |
| Date available:
|
2009-06-25T13:53:38Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128291 |
| . |
| Reference:
|
[1] Khuri, S. M.: Endomorphism rings and lattice isomorphism.J. Algebra 56 (2) (1979), 401–408. MR 0528584, 10.1016/0021-8693(79)90346-6 |
| Reference:
|
[2] Khuri, S. M.: Endomorphism rings of nonsingular modules.Ann. Sci. Math. Québec 4 (2) (1980), 145–152. Zbl 0451.16021, MR 0599052 |
| Reference:
|
[3] Khuri, S. M.: The endomorphism rings of a non-singular retractable module.East-West J. Math. 2 (2) (2000), 161–170. MR 1825452 |
| Reference:
|
[4] Rizvi, S. T., Roman, C. S.: Baer and quasi-Baer Modules.Comm. Algebra 32 (1) (2004), 103–123. Zbl 1072.16007, MR 2036224, 10.1081/AGB-120027854 |
| . |
