| Title:
|
On centralizers of semiprime rings (English) |
| Author:
|
Zalar, Borut |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
609-614 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Cal K$ be a semiprime ring and $T:\Cal K\rightarrow \Cal K$ an additive mapping such that $T(x^2)=T(x)x$ holds for all $x\in \Cal K$. Then $T$ is a left centralizer of $\Cal K$. It is also proved that Jordan centralizers and centralizers of $\Cal K$ coincide. (English) |
| Keyword:
|
semiprime ring |
| Keyword:
|
left centralizer |
| Keyword:
|
centralizer |
| Keyword:
|
Jordan centralizer |
| MSC:
|
16N60 |
| MSC:
|
16U70 |
| MSC:
|
16W10 |
| MSC:
|
16W20 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 0746.16011 |
| idMR:
|
MR1159807 |
| . |
| Date available:
|
2009-01-08T17:47:29Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118440 |
| . |
| Reference:
|
[1] Brešar M., Vukman J.: On some additive mapping in rings with involution.Aequationes Math. 38 (1989), 178-185. MR 1018911 |
| Reference:
|
[2] Brešar M., Zalar B.: On the structure of Jordan $\ast $-derivations.Colloquium Math., to appear. MR 1180629 |
| Reference:
|
[3] Herstein I.N.: Topics in ring theory.University of Chicago Press, 1969. Zbl 0232.16001, MR 0271135 |
| Reference:
|
[4] Herstein I.N.: Theory of rings.University of Chicago Press, 1961. |
| Reference:
|
[5] Johnson B.E., Sinclair A.M.: Continuity of derivations and a problem of Kaplansky.Amer. J. Math. 90 (1968), 1067-1073. Zbl 0179.18103, MR 0239419 |
| Reference:
|
[6] Šemrl P.: Quadratic functionals and Jordan $\ast $-derivations.Studia Math. 97 (1991), 157-165. MR 1100685 |
| . |
