| Title:
|
On left $(\theta,\varphi)$-derivations of prime rings (English) |
| Author:
|
Ashraf, Mohammad |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
157-166 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a $2$-torsion free prime ring. Suppose that $\theta , \phi $ are automorphisms of $R$. In the present paper it is established that if $R$ admits a nonzero Jordan left $(\theta ,\theta )$-derivation, then $R$ is commutative. Further, as an application of this resul it is shown that every Jordan left $(\theta ,\theta )$-derivation on $R$ is a left $(\theta ,\theta )$-derivation on $R$. Finally, in case of an arbitrary prime ring it is proved that if $R$ admits a left $(\theta ,\phi )$-derivation which acts also as a homomorphism (resp. anti-homomorphism) on a nonzero ideal of $R$, then $d=0$ on $R$. (English) |
| Keyword:
|
Lie ideals |
| Keyword:
|
prime rings |
| Keyword:
|
derivations |
| Keyword:
|
Jordan left derivations |
| Keyword:
|
left derivations |
| Keyword:
|
torsion free rings |
| MSC:
|
16N60 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 1114.16031 |
| idMR:
|
MR2164665 |
| . |
| Date available:
|
2008-06-06T22:45:37Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107946 |
| . |
| 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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| . |
