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A Generalization on Right Ideals of Prime Rings with α-Derivations

Year 2019, , 2190 - 2199, 01.12.2019

Barış Albayrak

https://doi.org/10.21597/jist.531856

Abstract

In this paper, we generalize previous studies on right ideals of prime ring 𝑅 with generalized 𝛼− derivation 𝐷 and show that 𝑅 is commutative under different conditions. Also, we investigate commutative property of prime ring 𝑅 for two generalized 𝛼− derivations 𝐷 and 𝐻.

Keywords

Prime ring Ideal Generalized α- derivation

References

  • Abu Nawas M. K, Al-Omary R. M, 2018. On ideals and commutativity of prime rings with generalized derivations. European Journal of Pure and Applied Mathematics, 11(1): 79-89.
  • Argac N, 2004. On near-rings with two-sided α- derivations. Turk. J.Math, 28: 195–204.
  • Ashraf M, Rehman N, 2001. On derivations and commutativity in prime rings. East-West J. Math., 3(1): 87-91.
  • Ashraf M, Asma A, Shakir A, 2007. Some commutativiy theorems for rings with generalized derivations. Southeast Asain Bull. of Math., 31:415-421.
  • Bresar M, 1991. On the distance of the composition of two derivations to the generalized derivations. Glaskow Math. J, 33: 89-93.
  • Chang J. C, 2009. Right generalized (α,β)- derivations having power central values. Taiwanese J. Math, 13(4): 1111-1120.
  • Gölbaşı Ö, Koç E, 2009. Notes on commutativity on prime rings with generalized derivation. Commun Fac. Sci. Univ. Ank. Series A1, 58(2): 39-46.
  • Herstein I. N, 1979. A note on derivations II. Canad. Math. Bull. 22: 509-511.
  • Mayne J. H, 1984. Centralizing mappings of prime rings. Canad. Math. Bull, 27: 122-126.
  • Posner E. C, 1957. Derivations in prime rings. Proc. Amer. Math. Soc. 8: 1093-1100.

α-Türevli Asal Halkaların Sağ İdealleri Üzerine Bir Genelleştirme

Year 2019, , 2190 - 2199, 01.12.2019

Barış Albayrak

https://doi.org/10.21597/jist.531856

Abstract

Bu makalede, genelleştirilmiş 𝛼− türevli 𝑅 asal halkasının sağ ideallerinde çalışılarak , 𝛼− türevli halkalardaki önceki çalışmalar genelleştirilmiş ve asal halkanın farklı durumlarda değişmeli olduğu gösterilmiştir. Bunlara ek olarak, iki genelleştirilmiş 𝛼− türev 𝐷 ve 𝐻 alınarak asal halkanın değişmelilik koşulları incelenmiştir.

Keywords

Asal halka İdeal Genelleşirilmiş 𝛼−türev

References

  • Abu Nawas M. K, Al-Omary R. M, 2018. On ideals and commutativity of prime rings with generalized derivations. European Journal of Pure and Applied Mathematics, 11(1): 79-89.
  • Argac N, 2004. On near-rings with two-sided α- derivations. Turk. J.Math, 28: 195–204.
  • Ashraf M, Rehman N, 2001. On derivations and commutativity in prime rings. East-West J. Math., 3(1): 87-91.
  • Ashraf M, Asma A, Shakir A, 2007. Some commutativiy theorems for rings with generalized derivations. Southeast Asain Bull. of Math., 31:415-421.
  • Bresar M, 1991. On the distance of the composition of two derivations to the generalized derivations. Glaskow Math. J, 33: 89-93.
  • Chang J. C, 2009. Right generalized (α,β)- derivations having power central values. Taiwanese J. Math, 13(4): 1111-1120.
  • Gölbaşı Ö, Koç E, 2009. Notes on commutativity on prime rings with generalized derivation. Commun Fac. Sci. Univ. Ank. Series A1, 58(2): 39-46.
  • Herstein I. N, 1979. A note on derivations II. Canad. Math. Bull. 22: 509-511.
  • Mayne J. H, 1984. Centralizing mappings of prime rings. Canad. Math. Bull, 27: 122-126.
  • Posner E. C, 1957. Derivations in prime rings. Proc. Amer. Math. Soc. 8: 1093-1100.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Barış Albayrak 0000-0002-8255-4706

Publication Date December 1, 2019
Submission Date February 25, 2019
Acceptance Date June 15, 2019
Published in Issue Year 2019

Cite

APA Albayrak, B. (2019). A Generalization on Right Ideals of Prime Rings with α-Derivations. Journal of the Institute of Science and Technology, 9(4), 2190-2199. https://doi.org/10.21597/jist.531856
AMA Albayrak B. A Generalization on Right Ideals of Prime Rings with α-Derivations. Iğdır Üniv. Fen Bil Enst. Der. December 2019;9(4):2190-2199. doi:10.21597/jist.531856
Chicago Albayrak, Barış. “A Generalization on Right Ideals of Prime Rings With α-Derivations”. Journal of the Institute of Science and Technology 9, no. 4 (December 2019): 2190-99. https://doi.org/10.21597/jist.531856.
EndNote Albayrak B (December 1, 2019) A Generalization on Right Ideals of Prime Rings with α-Derivations. Journal of the Institute of Science and Technology 9 4 2190–2199.
IEEE B. Albayrak, “A Generalization on Right Ideals of Prime Rings with α-Derivations”, Iğdır Üniv. Fen Bil Enst. Der., vol. 9, no. 4, pp. 2190–2199, 2019, doi: 10.21597/jist.531856.
ISNAD Albayrak, Barış. “A Generalization on Right Ideals of Prime Rings With α-Derivations”. Journal of the Institute of Science and Technology 9/4 (December 2019), 2190-2199. https://doi.org/10.21597/jist.531856.
JAMA Albayrak B. A Generalization on Right Ideals of Prime Rings with α-Derivations. Iğdır Üniv. Fen Bil Enst. Der. 2019;9:2190–2199.
MLA Albayrak, Barış. “A Generalization on Right Ideals of Prime Rings With α-Derivations”. Journal of the Institute of Science and Technology, vol. 9, no. 4, 2019, pp. 2190-9, doi:10.21597/jist.531856.
Vancouver Albayrak B. A Generalization on Right Ideals of Prime Rings with α-Derivations. Iğdır Üniv. Fen Bil Enst. Der. 2019;9(4):2190-9.