| Title:
|
Certain decompositions of matrices over Abelian rings (English) |
| Author:
|
Ashrafi, Nahid |
| Author:
|
Sheibani, Marjan |
| Author:
|
Chen, Huanyin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
417-425 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A ring $R$ is (weakly) nil clean provided that every element in $R$ is the sum of a (weak) idempotent and a nilpotent. We characterize nil and weakly nil matrix rings over abelian rings. Let $R$ be abelian, and let $n\in {\Bbb N}$. We prove that $M_n(R)$ is nil clean if and only if $R/J(R)$ is Boolean and $M_n(J(R))$ is nil. Furthermore, we prove that $R$ is weakly nil clean if and only if $R$ is periodic; $R/J(R)$ is ${\Bbb Z}_3$, $B$ or ${\Bbb Z}_3\oplus B$ where $B$ is a Boolean ring, and that $M_n(R)$ is weakly nil clean if and only if $M_n(R)$ is nil clean for all $n\geq 2$. (English) |
| Keyword:
|
idempotent element |
| Keyword:
|
nilpotent element |
| Keyword:
|
nil clean ring |
| Keyword:
|
weakly nil clean ring |
| MSC:
|
16E50 |
| MSC:
|
16S34 |
| MSC:
|
16U10 |
| idZBL:
|
Zbl 06738528 |
| idMR:
|
MR3661050 |
| DOI:
|
10.21136/CMJ.2017.0677-15 |
| . |
| Date available:
|
2017-06-01T14:28:49Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146765 |
| . |
| Reference:
|
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