| Title:
|
Centralizers on prime and semiprime rings (English) |
| Author:
|
Vukman, Joso |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
231-240 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let $R$ be a noncommutative prime ring of characteristic different from two and let $S$ and $T$ be left centralizers on $R$. Suppose that $[S(x),T(x)]S(x)+S(x)[S(x),T(x)]=0$ is fulfilled for all $x\in R$. If $S\neq 0$ $(T\neq 0)$ then there exists $\lambda $ from the extended centroid of $R$ such that $T=\lambda S$ $(S=\lambda T)$. (English) |
| Keyword:
|
prime ring |
| Keyword:
|
semiprime ring |
| Keyword:
|
extended centroid |
| Keyword:
|
derivation |
| Keyword:
|
Jordan derivation |
| Keyword:
|
left (right) centralizer |
| Keyword:
|
Jordan left (right) centralizer |
| Keyword:
|
commuting mapping |
| Keyword:
|
centralizing mapping |
| MSC:
|
16A12 |
| MSC:
|
16A68 |
| MSC:
|
16A72 |
| MSC:
|
16N60 |
| MSC:
|
16U70 |
| MSC:
|
16W10 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 0889.16016 |
| idMR:
|
MR1455489 |
| . |
| Date available:
|
2009-01-08T18:30:23Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118920 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
