| Title:
|
Free actions on semiprime rings (English) |
| Author:
|
Chaudhry, Muhammad Anwar |
| Author:
|
Samman, Mohammad S. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
197-208 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We identify some situations where mappings related to left centralizers, derivations and generalized $(\alpha ,\beta )$-derivations are free actions on semiprime rings. We show that for a left centralizer, or a derivation $T$, of a semiprime ring $R$ the mapping $\psi \: R \rightarrow R$ defined by $\psi (x)=T(x) x - x T(x)$ for all $x \in R$ is a free action. We also show that for a generalized $(\alpha , \beta )$-derivation $F$ of a semiprime ring $R,$ with associated $(\alpha , \beta )$-derivation $d,$ a dependent element $a$ of $F$ is also a dependent element of $\alpha + d.$ Furthermore, we prove that for a centralizer $f$ and a derivation $d$ of a semiprime ring $R$, $\psi = d\circ f$ is a free action. (English) |
| Keyword:
|
prime ring |
| Keyword:
|
semiprime ring |
| Keyword:
|
dependent element |
| Keyword:
|
free action |
| Keyword:
|
centralizer |
| Keyword:
|
derivation |
| MSC:
|
16N60 |
| MSC:
|
16W20 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 1170.16026 |
| idMR:
|
MR2428315 |
| DOI:
|
10.21136/MB.2008.134055 |
| . |
| Date available:
|
2009-09-24T22:36:20Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134055 |
| . |
| Reference:
|
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