| Title:
|
On Jordan ideals and derivations in rings with involution (English) |
| Author:
|
Oukhtite, Lahcen |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
389-395 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a $2$-torsion free $\ast$-prime ring, $d$ a derivation which commutes with $\ast$ and $J$ a $\ast$-Jordan ideal and a subring of $R$. In this paper, it is shown that if either $d$ acts as a homomorphism or as an anti-homomorphism on $J$, then $d=0$ or $J\subseteq Z(R)$. Furthermore, an example is given to demonstrate that the $\ast$-primeness hypothesis is not superfluous. (English) |
| Keyword:
|
$\ast$-prime rings |
| Keyword:
|
Jordan ideals |
| Keyword:
|
derivations |
| MSC:
|
16N16 |
| MSC:
|
16U70 |
| MSC:
|
16U80 |
| MSC:
|
16W10 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 1211.16037 |
| idMR:
|
MR2741872 |
| . |
| Date available:
|
2010-09-02T14:11:52Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140714 |
| . |
| Reference:
|
[1] Ashraf M., Ali A., Rehman N.: On Lie ideals with derivations as homomorphisms and anti-homomorphisms.Acta Math. Hungar. 101 (2003), 79–82. MR 2011464, 10.1023/B:AMHU.0000003893.61349.98 |
| Reference:
|
[2] Bell H.E., Kappe L.C.: Rings in which derivations satisfy certain algebraic conditions.Acta Math. Hungar. 53 (1989), 339–346. Zbl 0705.16021, MR 1014917, 10.1007/BF01953371 |
| Reference:
|
[3] Oukhtite L., Salhi S., Taoufiq L.: $\sigma$-Lie ideals with derivations as homomorphisms and anti-homomorphisms.Int. J. Algebra 1 (2007), no. 5, 235–239. Zbl 1124.16028, MR 2342996 |
| Reference:
|
[4] Oukhtite L., Salhi S.: On generalized derivations of $\sigma $-prime rings.Afr. Diaspora J. Math. 5 (2007), no. 1, 21–25. MR 2337187 |
| Reference:
|
[5] Zaidi S.M.A., Ashraf M., Ali S.: On Jordan ideals and left $(\theta ,\theta)$-derivations in prime rings.Int. J. Math. Math. Sci. 2004 (2004), no. 37–40, 1957–1964. Zbl 1069.16041, MR 2100888, 10.1155/S0161171204309075 |
| Reference:
|
[6] Posner E.C.: Derivations in prime rings.Proc. Amer. Math. Soc. 8 (1957), 1093–1100. Zbl 0082.03003, MR 0095863, 10.1090/S0002-9939-1957-0095863-0 |
| . |
