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Keywords:
Lie triple system; $(\varphi ,\psi )$-derivation; Jordan triple $(\varphi ,\psi )$-derivation; $\theta $-derivation; Jordan triple $\theta $-derivation
Lie triple system; $(\varphi ,\psi )$-derivation; Jordan triple $(\varphi ,\psi )$-derivation; $\theta $-derivation; Jordan triple $\theta $-derivation
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.
References:
[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. MR 1951117 | Zbl 1076.16512
[2] Bertram, W.: The Geometry of Jordan and Lie Structures. In: Lecture Notes in Math. vol. 1754, Springer-Verlag (2000). MR 1809879 | Zbl 1014.17024
[3] Brešar, M.: Jordan derivations on semiprime rings. Proc. Amer. Math. Soc. 104 (1988), 1003-1006. DOI 10.1090/S0002-9939-1988-0929422-1 | MR 0929422
[4] Brešar, M.: Jordan mappings of semiprime rings. J. Algebra 127 (1989), 218-228. DOI 10.1016/0021-8693(89)90285-8 | MR 1029414
[5] Brešar, M., Vukman, J.: Jordan $(\theta,\varphi)$-derivations. Glasnik Math. 46 (1991), 13-17. MR 1269170 | Zbl 0798.16023
[6] Hvala, B.: Generalized derivations in rings. Comm. Algebra. 26 (1998), 1147-1166. DOI 10.1080/00927879808826190 | MR 1612208 | Zbl 0899.16018
[7] Herstein, I. N.: Jordan derivations of prime rings. Proc. Amer. Math. Soc. 8 (1958), 1104-1110. DOI 10.1090/S0002-9939-1957-0095864-2 | MR 0095864 | Zbl 0216.07202
[8] Jacobson, N.: Lie and Jordan triple systems. Amer. J. Math. 71 (1949), 149-170. DOI 10.2307/2372102 | MR 0028305 | Zbl 0034.16903
[9] Jacobson, N.: General representation theory of Jordan algebras. Trans. Amer. Math. Soc. 70 (1951), 509-530. DOI 10.1090/S0002-9947-1951-0041118-9 | MR 0041118 | Zbl 0044.02503
[10] Jing, W., Lu, S.: Generalized Jordan derivations on prime rings and standard operator algebras. Taiwanese J. Math. 7 (2003), 605-613. DOI 10.11650/twjm/1500407580 | MR 2017914 | Zbl 1058.16031
[11] Lee, T.-K.: Generalized derivations of left faithful rings. Comm. Algebra. 27 (1999), 4057-4073. DOI 10.1080/00927879908826682 | MR 1700189 | Zbl 0946.16026
[12] Lister, W. G.: A structure theory of Lie triple systems. Trans. Amer. Math. Soc. 72 (1952), 217-242. DOI 10.1090/S0002-9947-1952-0045702-9 | MR 0045702 | Zbl 0046.03404
[13] Liu, C.-K., Shiue, W.-K.: Generalized Jordan triple $(\theta,\phi)$-derivations on semiprime rings. Taiwanese J. Math. 11 (2007), 1397-1406. DOI 10.11650/twjm/1500404872 | MR 2368657
[14] Vukman, J.: A note on generalized derivations of semiprime rings. Taiwanese J. Math. 11 (2007), 367-370. DOI 10.11650/twjm/1500404694 | MR 2333351 | Zbl 1124.16030
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