SOME RESULTS ON LEFT - JORDAN IDEALS AND ONE SIDED GENERALIZED DERIVATIONS

Abstract

Let R be a prime ring with characteristic not 2 and σ, τ, α, β, λ, µ, γ automorphisms of R. Let h : R −→ R be a nonzero left resp. right - generalized α, β − derivation associated with α, β − derivation d1 resp. d . Let W, V be nonzero left σ, τ −Jordan ideals of R and I a nonzero ideal of R. In this paper we also study the situations. 1 ah R b ⊂ Cλ,µ R 2 bh I, a σ,τ = 0 or h I, a σ,τ b = 0, 3 bh I ⊂ Cλ,µ W or h I b ⊂ Cλ,µ W , 4 h I ⊂ Cλ,µ J , 5 h R , a α,β ⊂ Cα,β R , 6 h I b, a λ,µ = 0, 7 bγ W ⊂ Cλ,µ V or γ W b ⊂ Cλ,µ V .

Keywords

• Prime ring,generalized derivation,- Jordan Ideal.

References

1. [1] Ashraf M. and Rehman N., (2002), On (σ, τ )−derivations in prime rings, Archivum Mathematicum, Vol. 38, No. 4.
2. [2] Aydın N. and Kaya K., (1992), Some Generalizations in Prime Rings with (σ, τ )−Derivation, Do˘ga-Tr. J. of Math. 16.
3. [3] Bresar M., (1991), On the distance of the composition of two derivation to generalized derivations , Glasgow Math. J, 33.
4. [4] Chang J. C., (2003), On the identity h(x) = af(x) + g(x)b, Taiwanese J. Math., 7, no.1.
5. [5] G¨uven E., (2018), One Left (σ, τ )−Jordan Ideals and One Sided Generalized Derivations, ICMMEORDU.
6. [6] G¨uven E., (2018), One Sided (σ, τ )−Lie Ideals and Generalized Derivations in Prime Rings, Palestine Journal of Mathematics, Vol. 7(2).
7. [7] G¨uven E., One Sided Generalized (σ, τ )−derivations on Rings, Bol. Soc. Paran. Mat., (to appear).
8. [8] Kaya K., Kandamar H. and Aydın N., (1993), Generalized Jordan Structure of Prime Rings, Tr. J. of Math.

9. [9] Mayne J. H., (1984), Centralizing Mappings of Prime Rings, Canad. Math. Bull., Vol. 27-1.