| Title:
|
Matrix rings with summand intersection property (English) |
| Author:
|
Karabacak, F. |
| Author:
|
Tercan, A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
621-626 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A ring $R$ has right SIP (SSP) if the intersection (sum) of two direct summands of $R$ is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of $R$ by $M$ has SIP if and only if $R$ has SIP and $(1-e)Me=0$ for every idempotent $e$ in $R$. Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP. (English) |
| Keyword:
|
modules |
| Keyword:
|
Summand Intersection Property |
| Keyword:
|
Morita invariant |
| MSC:
|
16D10 |
| MSC:
|
16D15 |
| MSC:
|
16D70 |
| MSC:
|
16S50 |
| idZBL:
|
Zbl 1080.16503 |
| idMR:
|
MR2000057 |
| . |
| Date available:
|
2009-09-24T11:05:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127827 |
| . |
| Reference:
|
[1] F. W. Anderson and K. R. Fuller: Rings and Categories of Modules.Springer-Verlag, 1974. MR 0417223 |
| Reference:
|
[2] G. F. Birkenmeier, J. Y. Kim and J. K. Park: When is the CS condition hereditary.Comm. Algebra 27 (1999), 3875–3885. MR 1699593, 10.1080/00927879908826670 |
| Reference:
|
[3] J. L. Garcia: Properties of direct summands of modules.Comm. Algebra 17 (1989), 73–92. Zbl 0659.16016, MR 0970864, 10.1080/00927878908823714 |
| Reference:
|
[4] K. R. Goodearl: Ring Theory.Marcel Dekker, 1976. Zbl 0336.16001, MR 0429962 |
| Reference:
|
[5] J. Hausen: Modules with the summand intersection property.Comm. Algebra 17 (1989), 135–148. Zbl 0667.16020, MR 0970868, 10.1080/00927878908823718 |
| Reference:
|
[6] I. Kaplansky: Infinite Abelian Groups.University of Michigan Press, 1969. Zbl 0194.04402, MR 0233887 |
| Reference:
|
[7] G. V. Wilson: Modules with the summand intersection property.Comm. Algebra 14 (1986), 21–38. Zbl 0592.13008, MR 0814137, 10.1080/00927878608823297 |
| . |
