Abstract
In this paper we describe generalized left (θ, φ)-derivations in prime
rings, and prove that an additive mapping in a ring R acting as a
homomorphism or anti-homomorphism on an additive subgroup S of
R must be either a mapping acting as a homomorphism on S or a
mapping acting as an anti-homomorphism on S, through which some
related 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
References
- 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.
Abstract
References
- 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.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | April 1, 2011 |
| Published in Issue | Year 2011 Volume: 40 Issue: 4 |