| Title:
|
An identity related to centralizers in semiprime rings (English) |
| Author:
|
Vukman, Joso |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
447-456 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to prove the following result: Let $R$ be a $2$-torsion free semiprime ring and let $T:R\rightarrow R$ be an additive mapping, such that $2T(x^2)=T(x)x+xT(x)$ holds for all $x\in R$. In this case $T$ is left and right centralizer. (English) |
| Keyword:
|
prime ring |
| Keyword:
|
semiprime ring |
| Keyword:
|
derivation |
| Keyword:
|
Jordan derivation |
| Keyword:
|
left (right) centralizer |
| Keyword:
|
left (right) Jordan centralizer |
| MSC:
|
16A12 |
| MSC:
|
16A68 |
| MSC:
|
16A72 |
| MSC:
|
16N60 |
| MSC:
|
16R50 |
| MSC:
|
16W10 |
| MSC:
|
16W20 |
| idZBL:
|
Zbl 1014.16021 |
| idMR:
|
MR1732490 |
| . |
| Date available:
|
2009-01-08T18:54:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119101 |
| . |
| Reference:
|
[1] Brešar M., Vukman J.: Jordan derivations on prime rings.Bull. Austral. Math. Soc. 37 (1988), 321-323. MR 0943433 |
| Reference:
|
[2] Brešar M.: Jordan derivations on semiprime rings.Proc. Amer. Math. Soc. 104 (1988), 1003-1006. MR 0929422 |
| Reference:
|
[3] Cusak J.: Jordan derivations on rings.Proc. Amer. Math. Soc. 53 (1975), 321-324. MR 0399182 |
| Reference:
|
[4] Herstein I.N.: Jordan derivations in prime rings.Proc. Amer. Math. Soc. 8 (1957), 1104-1110. MR 0095864 |
| Reference:
|
[5] Herstein I.N.: Rings with involution.Chicago Lectures in Math., Univ. of Chicago Press, Chicago, London, 1976. Zbl 0495.16007, MR 0442017 |
| Reference:
|
[6] Posner E.: Derivations in prime rings.Proc. Amer. Math. Soc. 8 (1957), 1093-1100. MR 0095863 |
| Reference:
|
[7] Vukman J.: Centralizers in prime and semiprime rings.Comment. Math. Univ. Carolinae 38 (1997), 231-240. MR 1455489 |
| Reference:
|
[8] Zalar B.: On centralizers of semiprime rings.Comment. Math. Univ. Carolinae 32 (1991), 609-614. Zbl 0746.16011, MR 1159807 |
| . |
