| Title:
|
Almost Abelian rings (English) |
| Author:
|
Wei, Junchao |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
21 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
15-30 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A ring $R$ is defined to be left almost Abelian if $ae=0$ implies $aRe=0$ for $a\in N(R)$ and $e\in E(R)$, where $E(R)$ and $N(R)$ stand respectively for the set of idempotents and the set of nilpotents of $R$. Some characterizations and properties of such rings are included. It follows that if $R$ is a left almost Abelian ring, then $R$ is $\pi $-regular if and only if $N(R)$ is an ideal of $R$ and $R/N(R)$ is regular. Moreover it is proved that (1) $R$ is an Abelian ring if and only if $R$ is a left almost Abelian left idempotent reflexive ring. (2) $R$ is strongly regular if and only if $R$ is regular and left almost Abelian. (3) A left almost Abelian clean ring is an exchange ring. (4) For a left almost Abelian ring $R$, it is an exchange $(S,2)$ ring if and only if $\mathbb Z/2\mathbb Z$ is not a homomorphic image of $R$. (English) |
| Keyword:
|
left almost Abelian rings |
| Keyword:
|
$\pi$-regular rings |
| Keyword:
|
Abelian rings |
| Keyword:
|
$(S,2)$ rings |
| MSC:
|
16A30 |
| MSC:
|
16A50 |
| MSC:
|
16D30 |
| MSC:
|
16E50 |
| idZBL:
|
Zbl 06202722 |
| idMR:
|
MR3067119 |
| . |
| Date available:
|
2013-07-18T15:24:27Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143346 |
| . |
| Reference:
|
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| . |
