| Title:
|
$\oplus$-cofinitely supplemented modules (English) |
| Author:
|
Çalışıcı, H. |
| Author:
|
Pancar, A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
1083-1088 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a ring and $M$ a right $R$-module. $M$ is called $ \oplus $-cofinitely supplemented if every submodule $N$ of $M$ with $\frac{M}{N}$ finitely generated has a supplement that is a direct summand of $M$. In this paper various properties of the $\oplus $-cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of $\oplus $-cofinitely supplemented modules is $\oplus $-cofinitely supplemented. (2) A ring $R$ is semiperfect if and only if every free $R$-module is $\oplus $-cofinitely supplemented. In addition, if $M$ has the summand sum property, then $M$ is $\oplus $-cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of $M$. (English) |
| Keyword:
|
cofinite submodule |
| Keyword:
|
$\oplus $-cofinitely supplemented module |
| MSC:
|
16D70 |
| MSC:
|
16D99 |
| idZBL:
|
Zbl 1080.16002 |
| idMR:
|
MR2100016 |
| . |
| Date available:
|
2009-09-24T11:20:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127953 |
| . |
| Reference:
|
[1] R. Alizade, G. Bilhan and P. F. Smith: Modules whose maximal submodules have supplements.Comm. Algebra 29 (2001), 2389–2405. MR 1845118, 10.1081/AGB-100002396 |
| Reference:
|
[2] J. L. Garcia: Properties of direct summands of modules.Comm. Algebra 17 (1989), 73–92. Zbl 0659.16016, MR 0970864, 10.1080/00927878908823714 |
| Reference:
|
[3] A. Harmanci, D. Keskin and P. F. Smith: On $ \oplus $-supplemented modules.Acta Math. Hungar. 83 (1999), 161–169. MR 1682909, 10.1023/A:1006627906283 |
| Reference:
|
[4] D. Keskin, P. F. Smith and W. Xue: Rings whose modules are $ \oplus $-supplemented.J. Algebra 218 (1999), 470–487. MR 1705802, 10.1006/jabr.1998.7830 |
| Reference:
|
[5] S. H. Mohamed B. J. Müller: Continuous and Discrete Modules. London Math. Soc. LNS Vol. 147.Cambridge Univ. Press, Cambridge, 1990. MR 1084376 |
| Reference:
|
[6] R. Wisbauer: Foundations of Module and Ring Theory.Gordon and Breach, Philadelphia, 1991. Zbl 0746.16001, MR 1144522 |
| Reference:
|
[7] H. Zöschinger: Komplementierte Moduln über Dedekindringen.J. Algebra 29 (1974), 42–56. MR 0340347, 10.1016/0021-8693(74)90109-4 |
| . |
