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Reverse and Jordan (α,β)- biderivation on Prime and Semiprime Rings

Year 2019, Volume: 9 Issue: 1, 149 - 164, 28.06.2019

Barış Albayrak , Neşet Aydın

https://izlik.org/JA78BY78ZX

Abstract

In this study, we prove that any nonzero reverse
(α,β)- biderivation on a prime ring is (α,β)- biderivation. Also, we show that
any Jordan (α,β)- biderivation on non-commutative semi-prime ring R with
char(R)≠2 is an (α,β)- biderivation. In addition, we investigate commutative
feature of prime ring with Jordan left α- biderivation.

Keywords

prime ring semi-prime ring reverse biderivation jordan biderivation

References

  • Referans1 Herstein I.N., Topics in Ring Theory, Univ. of Chicago Press, Chicago, 1969
  • Referans2 Bresar M., Jordan Derivations on semi-prime Rings, Proc. Amer. Math. Soc., 104, 1003-1006, 1988
  • Referans3 Herstein, I. N., On the Lie Structure of an Assosiative Rings, Journal of Algebra, 14, 561-571, 1970
  • Referans4 Hongan M., Rehman N., Al-Omary R. M., Lıe Ideals and Jordan Triple Derivations in Rings, Rend. Sem. Mat. Univ. Padova, 125, 147-156, 2011
  • Referans5 Bresar M., Vukman J.,Jordan Derivations on Prime Rings, Bull. Austral. Math. Soc., 37, 321-322, 1988
  • Referans6 Herstein I.N., Jordan Derivations of Prime Rings, Proc. Amer. Math. Soc., 8, 1104-1110, 1957
  • Referans7 Daif M. N., Haetinger C., Tammam El-Sayiad M. S., Reverse, Jordan and Left bi derivations, Oriental Journal of Mathematics, 2(2), 65-81, 2010
  • Referans8 Ashraf M., Rehman N., Ali S. and Mozumder R. M., On generalized (σ,τ)-bi derivations in rings, Asian-European Journal of Mathematics, 4(3), 389-402, 2011

Asal ve Yarıasal Halkalarda Ters ve Jordan (𝜶,𝜷)−bitürev

Year 2019, Volume: 9 Issue: 1, 149 - 164, 28.06.2019

Barış Albayrak , Neşet Aydın

https://izlik.org/JA78BY78ZX

Abstract

Bu çalışmada, asal halka üzerinde tanımlı sıfırdan farklı bir ters (𝛼,𝛽)− bitürevin aynı zamanda (𝛼,𝛽)− bitürev olduğu ispatlanmıştır. Ayrıca, 𝑐ℎ𝑎𝑟(𝑅)≠2 olacak biçimdeki değişmeli olmayan bir yarı-asal 𝑅 halkası üzerinde tanımlı Jordan (𝛼,𝛽)− bitürevin aynı zamanda (𝛼,𝛽)− bitürev olduğu gösterilmiştir. Bunların yanında, Jordan sol (𝛼,𝛼)−bitürevli asal halkaların değişmeli olma özellikleri araştırılmıştır.

Keywords

Asal halka Yarı-asal halka

References

  • Referans1 Herstein I.N., Topics in Ring Theory, Univ. of Chicago Press, Chicago, 1969
  • Referans2 Bresar M., Jordan Derivations on semi-prime Rings, Proc. Amer. Math. Soc., 104, 1003-1006, 1988
  • Referans3 Herstein, I. N., On the Lie Structure of an Assosiative Rings, Journal of Algebra, 14, 561-571, 1970
  • Referans4 Hongan M., Rehman N., Al-Omary R. M., Lıe Ideals and Jordan Triple Derivations in Rings, Rend. Sem. Mat. Univ. Padova, 125, 147-156, 2011
  • Referans5 Bresar M., Vukman J.,Jordan Derivations on Prime Rings, Bull. Austral. Math. Soc., 37, 321-322, 1988
  • Referans6 Herstein I.N., Jordan Derivations of Prime Rings, Proc. Amer. Math. Soc., 8, 1104-1110, 1957
  • Referans7 Daif M. N., Haetinger C., Tammam El-Sayiad M. S., Reverse, Jordan and Left bi derivations, Oriental Journal of Mathematics, 2(2), 65-81, 2010
  • Referans8 Ashraf M., Rehman N., Ali S. and Mozumder R. M., On generalized (σ,τ)-bi derivations in rings, Asian-European Journal of Mathematics, 4(3), 389-402, 2011
There are 8 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Barış Albayrak 0000-0002-8255-4706

Neşet Aydın This is me

Submission Date October 30, 2018
Acceptance Date June 2, 2019
Publication Date June 28, 2019
IZ https://izlik.org/JA78BY78ZX
Published in Issue Year 2019 Volume: 9 Issue: 1

Cite

APA Albayrak, B., & Aydın, N. (2019). Reverse and Jordan (α,β)- biderivation on Prime and Semiprime Rings. Adıyaman University Journal of Science, 9(1), 149-164. https://izlik.org/JA78BY78ZX
AMA 1.Albayrak B, Aydın N. Reverse and Jordan (α,β)- biderivation on Prime and Semiprime Rings. ADYU J SCI. 2019;9(1):149-164. https://izlik.org/JA78BY78ZX
Chicago Albayrak, Barış, and Neşet Aydın. 2019. “Reverse and Jordan (α,β)- Biderivation on Prime and Semiprime Rings”. Adıyaman University Journal of Science 9 (1): 149-64. https://izlik.org/JA78BY78ZX.
EndNote Albayrak B, Aydın N (June 1, 2019) Reverse and Jordan (α,β)- biderivation on Prime and Semiprime Rings. Adıyaman University Journal of Science 9 1 149–164.
IEEE [1]B. Albayrak and N. Aydın, “Reverse and Jordan (α,β)- biderivation on Prime and Semiprime Rings”, ADYU J SCI, vol. 9, no. 1, pp. 149–164, June 2019, [Online]. Available: https://izlik.org/JA78BY78ZX
ISNAD Albayrak, Barış - Aydın, Neşet. “Reverse and Jordan (α,β)- Biderivation on Prime and Semiprime Rings”. Adıyaman University Journal of Science 9/1 (June 1, 2019): 149-164. https://izlik.org/JA78BY78ZX.
JAMA 1.Albayrak B, Aydın N. Reverse and Jordan (α,β)- biderivation on Prime and Semiprime Rings. ADYU J SCI. 2019;9:149–164.
MLA Albayrak, Barış, and Neşet Aydın. “Reverse and Jordan (α,β)- Biderivation on Prime and Semiprime Rings”. Adıyaman University Journal of Science, vol. 9, no. 1, June 2019, pp. 149-64, https://izlik.org/JA78BY78ZX.
Vancouver 1.Barış Albayrak, Neşet Aydın. Reverse and Jordan (α,β)- biderivation on Prime and Semiprime Rings. ADYU J SCI [Internet]. 2019 Jun. 1;9(1):149-64. Available from: https://izlik.org/JA78BY78ZX

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