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, 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).
Keywords
References
- 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).
Abstract
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).
Keywords
References
- 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).
Details
| Primary Language | English |
|---|---|
| Journal Section | Mathematics |
| Authors | |
| Publication Date | June 28, 2019 |
| Submission Date | May 28, 2018 |
| Acceptance Date | May 26, 2019 |
| Published in Issue | Year 2019 Volume: 9 Issue: 1 |
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