Title:
|
On generalized Jordan derivations of Lie triple systems (English) |
Author:
|
Najati, Abbas |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
60 |
Issue:
|
2 |
Year:
|
2010 |
Pages:
|
541-547 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
Under some conditions we prove that every generalized Jordan triple derivation on a Lie triple system is a generalized derivation. Specially, we conclude that every Jordan triple $\theta $-derivation on a Lie triple system is a $\theta $-derivation. (English) |
Keyword:
|
Lie triple system |
Keyword:
|
$(\varphi ,\psi )$-derivation |
Keyword:
|
Jordan triple $(\varphi ,\psi )$-derivation |
Keyword:
|
$\theta $-derivation |
Keyword:
|
Jordan triple $\theta $-derivation |
MSC:
|
16W25 |
MSC:
|
17A36 |
MSC:
|
17A40 |
idZBL:
|
Zbl 1224.17008 |
idMR:
|
MR2657968 |
. |
Date available:
|
2010-07-20T16:57:52Z |
Last updated:
|
2020-07-03 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140588 |
. |
Reference:
|
[1] Ashraf, M., Al-Shammakh, Wafa S. M.: On generalized $(\theta,\phi)$-derivations in rings.Int. J. Math. Game Theory and Algebra 12 (2002), 295-300. Zbl 1076.16512, MR 1951117 |
Reference:
|
[2] Bertram, W.: The Geometry of Jordan and Lie Structures.In: Lecture Notes in Math. vol. 1754, Springer-Verlag (2000). Zbl 1014.17024, MR 1809879 |
Reference:
|
[3] Brešar, M.: Jordan derivations on semiprime rings.Proc. Amer. Math. Soc. 104 (1988), 1003-1006. MR 0929422, 10.1090/S0002-9939-1988-0929422-1 |
Reference:
|
[4] Brešar, M.: Jordan mappings of semiprime rings.J. Algebra 127 (1989), 218-228. MR 1029414, 10.1016/0021-8693(89)90285-8 |
Reference:
|
[5] Brešar, M., Vukman, J.: Jordan $(\theta,\varphi)$-derivations.Glasnik Math. 46 (1991), 13-17. Zbl 0798.16023, MR 1269170 |
Reference:
|
[6] Hvala, B.: Generalized derivations in rings.Comm. Algebra. 26 (1998), 1147-1166. Zbl 0899.16018, MR 1612208, 10.1080/00927879808826190 |
Reference:
|
[7] Herstein, I. N.: Jordan derivations of prime rings.Proc. Amer. Math. Soc. 8 (1958), 1104-1110. Zbl 0216.07202, MR 0095864, 10.1090/S0002-9939-1957-0095864-2 |
Reference:
|
[8] Jacobson, N.: Lie and Jordan triple systems.Amer. J. Math. 71 (1949), 149-170. Zbl 0034.16903, MR 0028305, 10.2307/2372102 |
Reference:
|
[9] Jacobson, N.: General representation theory of Jordan algebras.Trans. Amer. Math. Soc. 70 (1951), 509-530. Zbl 0044.02503, MR 0041118, 10.1090/S0002-9947-1951-0041118-9 |
Reference:
|
[10] Jing, W., Lu, S.: Generalized Jordan derivations on prime rings and standard operator algebras.Taiwanese J. Math. 7 (2003), 605-613. Zbl 1058.16031, MR 2017914, 10.11650/twjm/1500407580 |
Reference:
|
[11] Lee, T.-K.: Generalized derivations of left faithful rings.Comm. Algebra. 27 (1999), 4057-4073. Zbl 0946.16026, MR 1700189, 10.1080/00927879908826682 |
Reference:
|
[12] Lister, W. G.: A structure theory of Lie triple systems.Trans. Amer. Math. Soc. 72 (1952), 217-242. Zbl 0046.03404, MR 0045702, 10.1090/S0002-9947-1952-0045702-9 |
Reference:
|
[13] Liu, C.-K., Shiue, W.-K.: Generalized Jordan triple $(\theta,\phi)$-derivations on semiprime rings.Taiwanese J. Math. 11 (2007), 1397-1406. MR 2368657, 10.11650/twjm/1500404872 |
Reference:
|
[14] Vukman, J.: A note on generalized derivations of semiprime rings.Taiwanese J. Math. 11 (2007), 367-370. Zbl 1124.16030, MR 2333351, 10.11650/twjm/1500404694 |
. |