| Title:
|
Clean matrices over commutative rings (English) |
| Author:
|
Chen, Huanyin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
145-158 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A matrix $A\in M_n(R)$ is $e$-clean provided there exists an idempotent $E\in M_n(R)$ such that $A-E\in \mathop{\rm GL}_n(R)$ and $\det E=e$. We get a general criterion of $e$-cleanness for the matrix $[[a_1,a_2,\cdots ,a_{n+1}]]$. Under the $n$-stable range condition, it is shown that $[[a_1,a_2,\cdots ,a_{n+1}]]$ is $0$-clean iff $(a_1,a_2,\cdots ,a_{n+1})=1$. As an application, we prove that the $0$-cleanness and unit-regularity for such $n\times n$ matrix over a Dedekind domain coincide for all $n\geq 3$. The analogous for $(s,2)$ property is also obtained. (English) |
| Keyword:
|
matrix |
| Keyword:
|
clean element |
| Keyword:
|
unit-regularity |
| MSC:
|
15A23 |
| MSC:
|
16E50 |
| idZBL:
|
Zbl 1224.15034 |
| idMR:
|
MR2486621 |
| . |
| Date available:
|
2010-07-20T14:56:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140469 |
| . |
| Reference:
|
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| . |
