Lie ideals and Jordan triple (α,β)-derivations in rings

Year 2020, Volume: 69 Issue: 1, 528 - 539, 30.06.2020

Emine Koç Sögütcü , Nadeem ur Rehman

https://doi.org/10.31801/cfsuasmas.549472

Abstract

In this paper we prove that on a 2-torsion free semiprime ring R every Jordan triple (α,β)-derivation (resp. generalized Jordan triple (α,β)-derivation) on Lie ideal L is an (α,β)-derivation on L (resp. generalized (α,β)-derivation on L)

Keywords

Semiprime Rings , Lie ideals , Jordan triple (α.β)-derivations

References

• Ashraf, M., Ali, A. and Ali, Shakir, On Lie ideals and generalized (θ,φ)-derivations in prime rings, Comm. Algebra, 32, (2004), 2877-2785.
• Ashraf, M., Rehman, N. and Ali, Shakir, On Lie ideals and Jordan generalized derivations of prime rings, Indian J. Pure and Appl. math., 32(2), (2003), 291-294.
• Ashraf, M. and Rehman, N., On Jordan generalized derivations in rings, Math. J. Okayama Univ., 42, (2000), 7-9.
• J. Bergen, I. N. Herstein, and J. W. Kerr, Lie ideals and derivations of prime rings, J. Algebra, 71, (1981), 259-267.
• Bresar, M., On the distance of the compositions of two derivations to the generalized derivations, Glasgow Math. J., 33(1), (1991), 89-93.
• Bresar, M., Jordan mappings of semiprime rings, J. Algebra, 127, (1989), 218-228.
• Bresar, M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc., 104, (1988), 1003-1006.
• Bresar, M. and Vukman, J., Jordan derivations on prime rings, Bull. Austral. Math. Soc., 37, (1988), 321-322.
• Chuang, C, GPI's having coefficients in Utumi Quotient rings, Proc. Amer. Math. Soc., 103 (1988), 723-728.
• Cusack, J. M., Jordan derivations on rings, Proc. Amer. Math. Soc., 53, (1975), 321-324.
• Herstein, I. N., Topics in Ring Theory, Chicago Univ. Press, Chicago, 1969.
• Hongan, M., Rehman, N., Radwan, M. Lie ideals and Joudan Triple Derivations in rings, Rend. Sem. Mat. Univ. Padova, 125, (2011).
• Hvala, B., Generalized derivations in rings, Comm. Algebra, 26(1998), 1149-1166.
• Jing, W. and Lu, S., Generalized Jordan derivations on prime rings and standard operator algebras, Taiwanese J. Math., 7, (2003), 605-613.
• Liu, C. K. and Shiue, Q.K., Generalized Jordan triple (θ,φ)-derivations of semiprime rings, Taiwanese J. Math., 11, (2007), 1397-1406.
• Lanski, C. , Generalized derivations and nth power maps in rings, Comm. Algebra, 35, (2007), 3660-3672.
• Martindale III, W. S., Prime ring satisfying a generalized polynomial identity, J. Algebra, 12, (1969), 576-584.
• Molnar, L. , On centralizers of an H^{∗}-algebra, Publ. Math. Debrecen, 46, 1-2, (1995), 89-95, (2003), 277-283.
• Rehman, N. and Hongan, M., Generalized Jordan derivations on Lie ideals associate with Hochschild 2-cocycles of rings, Rend. Circ. Mat. Palermo, (2) 60, No. 3, (2011), 437-444.
• Vukman, J., A note on generalized derivations of semiprime rings, Taiwanese J. Math., 11, (2007), 367-370.
• Vukman, J. and Kosi-Ulbl, Irena, On centralizers of semiprime rings, Aequationes Math., 66, (2003), 277-283.
• Vukman, J., Centralizers of semiprime rings, Comment. Math. Univ. Carol., 42(2), (2001), 237-245.
• Vukman, J., An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolinae, 40(3), (1999), 447-456, 2, (2001), 237-245.
• Zalar, B., On centralizers of semiprime rings, Comment. Math. Univ. Carolinae, 32, (1991), 609-614.