Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 6 Sayı: 2, 41 - 48, 30.12.2023
https://doi.org/10.38061/idunas.1356057

Öz

Kaynakça

  • 1. Alharfie E. F., Muthana N. M. (2018). The commutativity of prime rings with homoderivations, Int. J. of Adv. and App. Sci., 5(5), 79-81.
  • 2. Awtar R. (1984). Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc., 90, 1, 9-14.
  • 3. Atteya M. J. (2022). Homogeneralized (σ,τ)-Derivations of Associative Rings, Studies on Scientific Developments in Geometry, Algebra, and Applied Mathematics, 52.
  • 4. Bergen J., Herstein I. N., Kerr J. (1981). Lie Ideals and derivations of Prime Rings, Journal of Algebra, 71, 259-267.
  • 5. Divinsky N. (1965). Rings and Radicals, University of Toronto Press, Toronto.
  • 6. Ebrahimi M. M., Pajoohesh H. (2003). Inner derivations and homoderivations on ϱ-Rings, Acta Math. Hungar., 100, 157-165.
  • 7. El-Soufi M. M. and Ghareeb A. (2022). Centrally Extended α-Homoderivations on Prime and Semiprime Rings, Journal of Mathematics.
  • 8. El Sofy, M. M. (2000). Rings with some kinds of mappings, M.Sc. Thesis, Cairo University, Branch of Fayoum, Egypt.
  • 9. Engin A., Aydın, N. (2023). Homoderivations in Prime Rings, Journal of New Theory, 43, 23-24.
  • 10. Güven E. (2019). Some Results on Left (σ,τ)-Jordan Ideals and one sided Generalized Derivations, TWMS J. App. and Eng. Math., 9, 1, 22-29.
  • 11. Herstein, I.N. (1979). A Note On Derivations II, Canad. Math. Bull., 22 (4), 509-511.
  • 12. Lee P. H., Lee T.K., (1981). On Derivations of Prime Rings Chinese Journal of Mathematics, 9, 2, 107-110.
  • 13. Mayne, J. H. (1984). Centralizing Mappings of Prime Rings, Canadian Mathematical Bulletin 27 (1), 122--126.
  • 14. Mouhssine S. and Boua A. (2021). Homoderivations and Semigroup Ideals in 3-Prime Near-Rings, Algebraic Str. and Their App. 8, No. 2, 177-194.
  • 15. Posner E. C. (1957). Derivations in prime rings, Proc. Amer. Math. Soc. 8, 1093-1100.
  • 16. Rehman N., Mozumder M. R., Abbasi A. (2019). Homoderivations on ideals of prime and semiprime rings, The Aligarh Bull. of Math., 38-1, 77-87.
  • 17. Aydın N., Kaya K. (1992). Some Generalizations in Prime Rings with (σ,τ)-Derivation, Doğa-Tr. J. Mathematics, 16, 169-176.
  • 18. Bresar M. (1991). On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J., 33, 89-93.

Homoderivations and Their Impact on Lie Ideals in Prime Rings

Yıl 2023, Cilt: 6 Sayı: 2, 41 - 48, 30.12.2023
https://doi.org/10.38061/idunas.1356057

Öz

Assume we have a prime ring denoted as $R$, with a characteristic distinct from two. The concept of a homoderivation refers to an additive map $Η$ of a ring $R$ that satisfies the property $Η(r_1 r_2 )=Η(r_1 ) r_2+r_1 Η(r_2 )+Η(r_1 )Η(r_2 )$, $\forall r_1,r_2 \in R$. This article aims to obtain results for prime rings, ideals, and Lie ideals by utilizing the concept of homoderivation in conjunction with the established theory of derivations.

Kaynakça

  • 1. Alharfie E. F., Muthana N. M. (2018). The commutativity of prime rings with homoderivations, Int. J. of Adv. and App. Sci., 5(5), 79-81.
  • 2. Awtar R. (1984). Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc., 90, 1, 9-14.
  • 3. Atteya M. J. (2022). Homogeneralized (σ,τ)-Derivations of Associative Rings, Studies on Scientific Developments in Geometry, Algebra, and Applied Mathematics, 52.
  • 4. Bergen J., Herstein I. N., Kerr J. (1981). Lie Ideals and derivations of Prime Rings, Journal of Algebra, 71, 259-267.
  • 5. Divinsky N. (1965). Rings and Radicals, University of Toronto Press, Toronto.
  • 6. Ebrahimi M. M., Pajoohesh H. (2003). Inner derivations and homoderivations on ϱ-Rings, Acta Math. Hungar., 100, 157-165.
  • 7. El-Soufi M. M. and Ghareeb A. (2022). Centrally Extended α-Homoderivations on Prime and Semiprime Rings, Journal of Mathematics.
  • 8. El Sofy, M. M. (2000). Rings with some kinds of mappings, M.Sc. Thesis, Cairo University, Branch of Fayoum, Egypt.
  • 9. Engin A., Aydın, N. (2023). Homoderivations in Prime Rings, Journal of New Theory, 43, 23-24.
  • 10. Güven E. (2019). Some Results on Left (σ,τ)-Jordan Ideals and one sided Generalized Derivations, TWMS J. App. and Eng. Math., 9, 1, 22-29.
  • 11. Herstein, I.N. (1979). A Note On Derivations II, Canad. Math. Bull., 22 (4), 509-511.
  • 12. Lee P. H., Lee T.K., (1981). On Derivations of Prime Rings Chinese Journal of Mathematics, 9, 2, 107-110.
  • 13. Mayne, J. H. (1984). Centralizing Mappings of Prime Rings, Canadian Mathematical Bulletin 27 (1), 122--126.
  • 14. Mouhssine S. and Boua A. (2021). Homoderivations and Semigroup Ideals in 3-Prime Near-Rings, Algebraic Str. and Their App. 8, No. 2, 177-194.
  • 15. Posner E. C. (1957). Derivations in prime rings, Proc. Amer. Math. Soc. 8, 1093-1100.
  • 16. Rehman N., Mozumder M. R., Abbasi A. (2019). Homoderivations on ideals of prime and semiprime rings, The Aligarh Bull. of Math., 38-1, 77-87.
  • 17. Aydın N., Kaya K. (1992). Some Generalizations in Prime Rings with (σ,τ)-Derivation, Doğa-Tr. J. Mathematics, 16, 169-176.
  • 18. Bresar M. (1991). On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J., 33, 89-93.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
Bölüm Makaleler
Yazarlar

Evrim Güven 0000-0001-5256-4447

Yayımlanma Tarihi 30 Aralık 2023
Kabul Tarihi 2 Ekim 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 2

Kaynak Göster

APA Güven, E. (2023). Homoderivations and Their Impact on Lie Ideals in Prime Rings. Natural and Applied Sciences Journal, 6(2), 41-48. https://doi.org/10.38061/idunas.1356057