Xiao-wei XU, Hong-ying ZHANG

A Note on Generalized Left (t, p)-Derivations in Prime Rings

In this paper we describe generalized left (θ, φ)-derivations in primerings, and prove that an additive mapping in a ring R acting as ahomomorphism or anti-homomorphism on an additive subgroup S ofR must be either a mapping acting as a homomorphism on S or amapping acting as an anti-homomorphism on S, through which somerelated results are improved.

Keywords:

Prime rings, Generalized left (θ, Mappings acting as homomorphisms, Mappings acting as anti-homomorphisms Mappings acting as homomorphisms or anti-homomorphisms, 2000 AMS Classification: 16 W 25,

PDF

___

Ali, A. and Kumar, D. Generalized derivations as homomorphisms or as anti-homo- morphisms in a prime ring, Hacet. J. Math. Stat. 38 (1), 17–20, 2009.
Ashraf, M. On left (θ, φ)-derivations of prime rings, Arch. Math. (Brno) 41, 157–166, 2005. [3] Ashraf, M., Ali, A. and Ali, S. On Lie ideals and generalized (θ, φ)-derivations in prime rings, Comm. Algebra 32, 2977–2985, 2004.
Ashraf, M. and Ali, S. On generalized Jordan left derivations in rings, Bull. Korean Math. Soc. 45, 253–261, 2008.
Bell, H. E. and Kappe, L. C. Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungar. 53, 339–346, 1989.
Breˇsar, M. On the distance of the composition of two derivations to the generalized deriva- tions, Glasgow Math. 33, 89–93, 1991.
Breˇsar, M. and Vukman, J. On left derivations and related mappings, Proc. Amer. Math. Soc. 110, 7–16, 1990.
Chang, J. C. and Lin, J. S. (α, β)-derivation with nilpotent values, Chin. J. Math. 22, 349– 355, 1994.
Cheng, H. W. and Wei, F. Generalized skew derivations of rings, Adv. Math. (China) 35, 237–243, 2006. [10] Hvala, B. Generalized derivations in rings, Comm. Algebra 26, 1147–1166, 1998.
Lee, T. K. Generalized derivations of left faithful rings, Comm. Algebra 27, 4057–4073, 1999.
Zaidi, S. M. A., Ashraf, M. and Ali, S. On Jordan ideals and left (θ, θ)-derivations in prime rings, Int. J. Math. & Math. Sci. 37, 1957–1964, 2004.