| Title:
|
Commutativity theorems for rings with differential identities on Jordan ideals (English) |
| Author:
|
Oukhtite, L. |
| Author:
|
Mamouni, A. |
| Author:
|
Ashraf, Mohammad |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
447-457 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate commutativity of ring $R$ with involution $'\ast'$ which admits a derivation satisfying certain algebraic identities on Jordan ideals of $R$. Some related results for prime rings are also discussed. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous. (English) |
| Keyword:
|
derivation |
| Keyword:
|
generalized derivation |
| Keyword:
|
$*$-Jordan ideal |
| Keyword:
|
commutativity theorems |
| MSC:
|
16N60 |
| MSC:
|
16R50 |
| MSC:
|
16U70 |
| MSC:
|
16U80 |
| MSC:
|
16W10 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 1299.16018 |
| idMR:
|
MR3125069 |
| . |
| Date available:
|
2013-10-01T21:09:12Z |
| Last updated:
|
2016-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143468 |
| . |
| Reference:
|
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| Reference:
|
[2] Bell H.E., Daif M.N.: On derivations and commutativity in prime rings.Acta Math. Hungar. 66 (1995), 337–343. Zbl 0822.16033, MR 1314011, 10.1007/BF01876049 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Herstein I.N.: A note on derivations.Canad. Math. Bull. 21 (1978), 369–370. Zbl 0434.16027, MR 0506447, 10.4153/CMB-1978-065-x |
| Reference:
|
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| Reference:
|
[7] Mamouni A., Oukhtite L.: Derivations satisfying certain algebraic identities on Jordan ideals.Arab. J. Math. 1 (2012), no. 3, 341–346. MR 3041071, 10.1007/s40065-012-0039-9 |
| Reference:
|
[8] Mamouni A., Oukhtite L.: Generalized derivations centralizing on Jordan ideals of rings with involution.submitted. |
| Reference:
|
[9] Oukhtite L.: On Jordan ideals and derivations in rings with involution.Comment. Math. Univ. Carolin. 51 (2010), no. 3, 389–395. Zbl 1211.16037, MR 2741872 |
| Reference:
|
[10] Oukhtite L.: Posner's second theorem for Jordan ideals in rings with involution.Expo. Math. 29 (2011), 415–419. Zbl 1232.16027, MR 2861767, 10.1016/j.exmath.2011.07.002 |
| Reference:
|
[11] Oukhtite L., Salhi S.: On derivations in $\sigma$-prime rings.Int. J. Algebra 1 (2007), no. 5, 241–246. Zbl 1124.16025, MR 2342997 |
| Reference:
|
[12] Zaidi S.M.A., Ashraf A., Ali S.: On Jordan ideals and left $(\theta ,\theta)$-derivations in prime rings.Int. J. Math. Math. Sci. 2004, no. 37–40, 1957–1964. Zbl 1069.16041, MR 2100888, 10.1155/S0161171204309075 |
| . |
