On Right (σ, τ)-Jordan Ideals and One Sided Generalized Derivations

Yıl 2019, Cilt: 9 Sayı: 1, 1 - 12, 28.06.2019

Evrim Güven

Öz

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, bÎR and U, V nonzero right (σ,τ)-Jordan ideals of R. In
this article we  have investigated the
following situations:

(1)
bh(γ(U))=0, (2) h(γ(U))b=0,  (3) h(γ(U))=0,
(4) UÌC
_λ,µ(V), (5) bh(I)Ì

C
_λ,µ(U) or h(I)bÌC _λ,µ(U), (6) bVÌC _λ,µ(U)
or VbÌC
_λ,µ(U).

Anahtar Kelimeler

Prime Ring, Generalized Derivation

Sağ (σ,τ)-Jordan İdealler ve Tek Yanlı Genelleştirilmiş Türevler Üzerine

Öz

R, karakteristiği 2 den farklı
bir asal halka ve σ,τ,α,β,λ,μ,γ dönüşümleri R üzerinde otomorfizmler olsunlar.
h:R→R sıfırdan farklı bir sol (sağ)-genelleştirilmiş (α,β)-türev, b∈R ve U ile V, R halkasının sıfırdan farklı sağ
(σ,τ)-Jordan idealleri olsunlar. Bu makalede, aşağıdaki durumları araştırdık:

(1)
bh(γ(U))=0, (2) h(γ(U))b=0,  (3)
h(γ(U))=0, (4) UÌC
_λ,µ(V), (5) bh(I)Ì

C
_λ,µ(U) or h(I)bÌC _λ,µ(U), (6) bVÌC _λ,µ(U)
or VbÌC
_λ,µ(U).

Anahtar Kelimeler

Asal Halka, Genelleştirilmiş Türev

Kaynakça

• Aydın N. and Kaya K., Some Generalizations in Prime Rings with (σ,τ)-Derivation, Doğa-Tr. J. of Math., 16, (1992). Bresar M., On the Distance of the Composition of Two Derivation to Generalized Derivations, Glasgow Math.J, 33, (1991). Chang J. C., On the Identity h(x)=af(x)+g(x)b, Taiwanese J. Math., 7, no.1, (2003). Güven E., One Sided (σ,τ)-Lie Ideals and Generalized Derivations in Prime Rings, Palestine Journal of Mathematics, (to appear). Güven E., One Sided Generalized (σ,τ)-Derivations in Rings, Boletim Sociedade Paranaense de Matemática, (to appear). Kandamar H. and Kaya K, (σ,τ)-Right Jordan Ideals, C.Ü. Fen Bil. Derg., (1993). Kaya K., Kandamar H. and Aydın N., Generalized Jordan Structure of Prime Rings, Tr.J.of Math. (1993). Kaya K., On Prime Rings with (σ,τ)-Derivations, Doga, TU MAT. D.C. 12, 2, (1988). Mayne J. H., Centralizing Mappings of Prime Rings, Canad. Math. Bull., 27, (1984). Zaidi S. M. A. Ashraf, M. and Ali S. On Jordan Ideals and Left (θ,θ)-Derivations, in Prime Rings, Internat. J. of Math. and Math. Sci., 37, (2004).