| Title:
|
Strong separativity over exchange rings (English) |
| Author:
|
Chen, Huanyin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
417-428 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An exchange ring $R$ is strongly separative provided that for all finitely generated projective right $R$-modules $A$ and $B$, $A\oplus A\cong A \oplus B\Rightarrow A\cong B$. We prove that an exchange ring $R$ is strongly separative if and only if for any corner $S$ of $R$, $aS+bS=S$ implies that there exist $u,v\in S$ such that $au=bv$ and $Su+Sv=S$ if and only if for any corner $S$ of $R$, $aS+bS=S$ implies that there exists a right invertible matrix $\begin{pmatrix} a&b\\ *&* \end{pmatrix} \in M_2(S)$. The dual assertions are also proved. (English) |
| Keyword:
|
strong separativity |
| Keyword:
|
exchange ring |
| Keyword:
|
regular ring |
| MSC:
|
16D70 |
| MSC:
|
16E50 |
| MSC:
|
19B10 |
| MSC:
|
19E99 |
| idZBL:
|
Zbl 1166.16002 |
| idMR:
|
MR2411098 |
| . |
| Date available:
|
2009-09-24T11:55:41Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128266 |
| . |
| Reference:
|
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| Reference:
|
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| . |
