| Title:
|
On Lie ideals and Jordan left derivations of prime rings (English) |
| Author:
|
Ashraf, Mohammad |
| Author:
|
Nadeem-ur-Rehman |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
201-206 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a 2-torsion free prime ring and let $U$ be a Lie ideal of $R$ such that $u^{2} \in U$ for all $u \in U$. In the present paper it is shown that if $d$ is an additive mappings of $R$ into itself satisfying $d(u^{2})=2ud(u)$ for all $u \in U$, then $d(uv)=ud(v)+vd(u)$ for all $u,v \in U$. (English) |
| Keyword:
|
Lie ideals |
| Keyword:
|
prime rings |
| Keyword:
|
Jordan left derivations |
| Keyword:
|
left derivations |
| Keyword:
|
torsion free rings |
| MSC:
|
16N60 |
| MSC:
|
16W10 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 1030.16018 |
| idMR:
|
MR1785037 |
| . |
| Date available:
|
2008-06-06T22:25:50Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107732 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Bresar M., Vukman J.: Jordan derivations of prime rings.Bull. Aust. Math. Soc. 37 (1988), 321–322. MR 0943433 |
| Reference:
|
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| Reference:
|
[6] Deng Q.: On Jordan left derivations.Math. J. Okayama Univ. 34 (1992), 145–147. Zbl 0813.16021, MR 1272614 |
| Reference:
|
[7] Herstein I. N.: Jordan derivations of prime rings.Proc. Amer. Math. Soc. 8 (1957), 1104–1110. MR 0095864 |
| Reference:
|
[8] Herstein I. N.: Topics in ring theory.Univ. of Chcago Press, Chicago 1969. Zbl 0232.16001, MR 0271135 |
| Reference:
|
[9] Kill-Wong Jun, Byung-Do Kim: A note on Jordan left derivations.Bull. Korean Math. Soc. 33 (1996) No. 2, 221–228. MR 1405475 |
| Reference:
|
[10] Posner E. C.: Derivations in prime rings.Proc. Amer. Math. Soc. 8 (1957), 1093–1100. MR 0095863 |
| Reference:
|
[11] Vukman J.: Jordan left derivations on semiprime rings.Math. J. Okayama Univ. (to appear). Zbl 0937.16044, MR 1680747 |
| . |
