| Title:
|
Exchange rings with stable range one (English) |
| Author:
|
Chen, Huanyin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
579-590 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize exchange rings having stable range one. An exchange ring $R$ has stable range one if and only if for any regular $a\in R$, there exist an $e\in E(R)$ and a $u\in U(R)$ such that $a=e+u$ and $aR\cap eR=0$ if and only if for any regular $a\in R$, there exist $e\in r.ann(a^+)$ and $u\in U(R)$ such that $a=e+u$ if and only if for any $a,b\in R$, $R/aR\cong R/bR\Longrightarrow aR\cong bR$. (English) |
| Keyword:
|
exchange ring |
| Keyword:
|
stable range one |
| Keyword:
|
idempotent |
| Keyword:
|
unit |
| MSC:
|
16D70 |
| MSC:
|
16E20 |
| MSC:
|
16E50 |
| MSC:
|
16U99 |
| MSC:
|
19B10 |
| idZBL:
|
Zbl 1161.16008 |
| idMR:
|
MR2337616 |
| . |
| Date available:
|
2009-09-24T11:47:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128191 |
| . |
| Reference:
|
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| . |
