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Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings

Yıl 2020, Cilt: 10 Sayı: 1, 264 - 272, 25.06.2020

Emine Koç Sögütcü Öznur Gölbaşı

https://doi.org/10.37094/adyujsci.563317

Öz

Let R be a 3!-torsion free semiprime ring, τ, σ two endomorphisms of R, d:R→R an additive mapping and L be a noncentral square-closed Lie ideal of R . An additive mapping d:R→R is said to be a Jordan (σ,τ)-derivation if d(x²)=d(x)σ(x)+τ(x)d(x) holds for all x,y∈R. Also, d is called a Jordan triple (σ,τ)-derivation if d(xyx)=d(x)σ(yx)+τ(x)d(y)σ(x)+τ(xy)d(x), for all x,y∈R. In this paper, we proved the following result: d is a Jordan (σ,τ)-derivation if and only if d is a Jordan triple (σ,τ)-derivation.

Anahtar Kelimeler

Semiprime ring Jordan derivation Jordan triple derivation (σ τ)-derivation Jordan (σ τ)-derivation Jordan triple (σ τ)-derivation

Destekleyen Kurum

Cübap

Proje Numarası

F563

Kaynakça

  • [1] Herstein, I.N., Jordan derivations of prime rings, Proceedings of the American Mathematical Society, 8, 1104-1110, 1957.
  • [2] Cusack, J.M., Jordan derivations on rings, Proceedings of the American Mathematical Society, 53, 321-324, 1975.
  • [3] Gupta, V., Jordan derivations on Lie ideals of prime and semiprime rings, East-West Journal of Mathematics, 9 (1), 47-51, 2007.
  • [4] Jing, W., Lu, S., Generalized Jordan derivations on prime rings and standard opetaror algebras, Taiwanese Journal of Mathematics, 7, 605-613, 2003.
  • [5] Vukman, J., A note on generalized derivations of semiprime rings, Taiwanese Journal of Mathematics, 11, 367-370., 2007.
  • [6] Rehman, N., Koç Sögütcü, E., Lie idelas and Jordan Triple (α,β)-derivations in rings, Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics, 69(1), 528-539, 2020. (doi: 10.31801/cfsuasmas.549472)
  • [7] Herstein, I.N., Topics in ring theory, The University of Chicago Press, Chicago, London, 1969.
  • [8] Bresar, M., Jordan mappings of semiprime rings, Journal of Algebra, 127, 218-228, 1989.
  • [9] Fošner, M., Ilišević, D., On Jordan triple derivations and related mappings, Mediterranean. Journal of Mathematics, 5, 415-427, 2008.
  • [10] Hongan, M., Rehman, N., Al-Omary, R. M., Lie ideals and Jordan triple derivations in rings, Rendiconti del Seminario Matematico della Università di Padova, 125,147-156, 2011. (doi: 10.4171/RSMUP/125-9).

Yarıasal halkalarda Jordan (σ,τ)- Türevler ve Jordan Üçlü (σ,τ)-Türevlerin Karşılaştırılması

Yıl 2020, Cilt: 10 Sayı: 1, 264 - 272, 25.06.2020

Emine Koç Sögütcü Öznur Gölbaşı

https://doi.org/10.37094/adyujsci.563317

Öz

R bir 3!-torsion free yarıasal halka, � ve � iki endomorfizm, �: � → � toplamsal dönüşüm ve L merkez tarafından kapsanmayan R halkasının bir kare kapalı Lie ideali olsun. �: � → �toplamsal dönüşümü her �, � ∈ � için �(�²) = �(�)�(�) + �(�)�(�) koşulunu sağlıyorsa d dönüşümüne Jordan (�, �) −türev denir. Ayrıca, �: � → � toplamsal dönüşümü her �, � ∈ � için �(���) = �(�)�(��) + �(�)�(�)�(�) + �(��)�(�) koşulunu sağlıyorsa d dönüşümüne Jordan üçlü (�, �) −türev denir. Bu çalışmada, d bir L üzerinde Jordan (�, �) −türev olması için gerek ve yeter koşul d dönüşümünün L üzerinde Jordan üçlü (�, �) −türev olmasıdır sonucu ispatlanmıştır.

Anahtar Kelimeler

Yarıasal halka Jordan türev Jordan üçlü türev (σ, τ) −türev Jordan (σ, τ) −türev Jordan üçlü (σ, τ) −türev

Proje Numarası

F563

Kaynakça

  • [1] Herstein, I.N., Jordan derivations of prime rings, Proceedings of the American Mathematical Society, 8, 1104-1110, 1957.
  • [2] Cusack, J.M., Jordan derivations on rings, Proceedings of the American Mathematical Society, 53, 321-324, 1975.
  • [3] Gupta, V., Jordan derivations on Lie ideals of prime and semiprime rings, East-West Journal of Mathematics, 9 (1), 47-51, 2007.
  • [4] Jing, W., Lu, S., Generalized Jordan derivations on prime rings and standard opetaror algebras, Taiwanese Journal of Mathematics, 7, 605-613, 2003.
  • [5] Vukman, J., A note on generalized derivations of semiprime rings, Taiwanese Journal of Mathematics, 11, 367-370., 2007.
  • [6] Rehman, N., Koç Sögütcü, E., Lie idelas and Jordan Triple (α,β)-derivations in rings, Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics, 69(1), 528-539, 2020. (doi: 10.31801/cfsuasmas.549472)
  • [7] Herstein, I.N., Topics in ring theory, The University of Chicago Press, Chicago, London, 1969.
  • [8] Bresar, M., Jordan mappings of semiprime rings, Journal of Algebra, 127, 218-228, 1989.
  • [9] Fošner, M., Ilišević, D., On Jordan triple derivations and related mappings, Mediterranean. Journal of Mathematics, 5, 415-427, 2008.
  • [10] Hongan, M., Rehman, N., Al-Omary, R. M., Lie ideals and Jordan triple derivations in rings, Rendiconti del Seminario Matematico della Università di Padova, 125,147-156, 2011. (doi: 10.4171/RSMUP/125-9).
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Emine Koç Sögütcü 0000-0002-8328-4293

Öznur Gölbaşı 0000-0002-9338-6170

Proje Numarası F563
Yayımlanma Tarihi 25 Haziran 2020
Gönderilme Tarihi 11 Mayıs 2019
Kabul Tarihi 21 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 1

Kaynak Göster

APA Koç Sögütcü, E., & Gölbaşı, Ö. (2020). Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings. Adıyaman University Journal of Science, 10(1), 264-272. https://doi.org/10.37094/adyujsci.563317
AMA Koç Sögütcü E, Gölbaşı Ö. Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings. ADYU J SCI. Haziran 2020;10(1):264-272. doi:10.37094/adyujsci.563317
Chicago Koç Sögütcü, Emine, ve Öznur Gölbaşı. “Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings”. Adıyaman University Journal of Science 10, sy. 1 (Haziran 2020): 264-72. https://doi.org/10.37094/adyujsci.563317.
EndNote Koç Sögütcü E, Gölbaşı Ö (01 Haziran 2020) Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings. Adıyaman University Journal of Science 10 1 264–272.
IEEE E. Koç Sögütcü ve Ö. Gölbaşı, “Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings”, ADYU J SCI, c. 10, sy. 1, ss. 264–272, 2020, doi: 10.37094/adyujsci.563317.
ISNAD Koç Sögütcü, Emine - Gölbaşı, Öznur. “Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings”. Adıyaman University Journal of Science 10/1 (Haziran 2020), 264-272. https://doi.org/10.37094/adyujsci.563317.
JAMA Koç Sögütcü E, Gölbaşı Ö. Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings. ADYU J SCI. 2020;10:264–272.
MLA Koç Sögütcü, Emine ve Öznur Gölbaşı. “Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings”. Adıyaman University Journal of Science, c. 10, sy. 1, 2020, ss. 264-72, doi:10.37094/adyujsci.563317.
Vancouver Koç Sögütcü E, Gölbaşı Ö. Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings. ADYU J SCI. 2020;10(1):264-72.
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