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Journals / Hacettepe Journal of Mathematics and Statistics / 2015 / Cilt: 44 - Sayı: 1

On centralizing automorphisms and Jordan left derivations on σ-prime gamma rings

Kalyan Kumar DEY
Akhil Chandra PAUL
Bijan DAVVAZ
Pages
51–57
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We also study the additive maps d :M → M such that d(uαu) = 2uαd(u), where u ∈ U and α ∈Γ, and show that d(uαv) = uαd(v)+vαd(u), for all u,v ∈ U and α ∈Γ. 2000 AMS Classification: 16W10, 16W25, 16W20, 16U80.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let M be a 2-torsion free σ-prime Γ-ring and U be a non-zero σ-square closed Lie ideal of M.
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Key Findings & Data:If T : M → M is an automorphism on U such that T ?= 1 and Tσ = σT on U, then we prove that U ⊆ Z(M).
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Conclusion & Impact:We also study the additive maps d :M → M such that d(uαu) = 2uαd(u), where u ∈ U and α ∈Γ, and show that d(uαv) = uαd(v)+vαd(u), for all u,v ∈ U and α ∈Γ. 2000 AMS Classification: 16W10, 16W25, 16W20, 16U80.
🔬Design:Research Article
📍Scope:2000 Verileri
⚙️Variables:Domain Parameters

Abstract

Let M be a 2-torsion free σ-prime Γ-ring and U be a non-zero σ-square closed Lie ideal of M. If T : M → M is an automorphism on U such that T ?= 1 and Tσ = σT on U, then we prove that U ⊆ Z(M). We also study the additive maps d :M → M such that d(uαu) = 2uαd(u), where u ∈ U and α ∈Γ, and show that d(uαv) = uαd(v)+vαd(u), for all u,v ∈ U and α ∈Γ. 2000 AMS Classification: 16W10, 16W25, 16W20, 16U80.

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Cite This Article

DEY, K. K., PAUL, A. C., DAVVAZ, B. (2022). On centralizing automorphisms and Jordan left derivations on σ-prime gamma rings. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 1, 51–57. https://ajindex.com/articles/530251

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References (15)

  1. M. Ashraf and N. Rehman, On Lie ideals and Jourdan left derivations of prime rings, Archivum Math., 36 (2000) 201-206
  2. W. E. Barnes, On the Γ-rings of Nobusawa, Pacific J. Math., 18 (1966), 411-422
  3. Y. Ceven, Jordan left derivations on completely prime Γ-ring, C.U. Fen-Edebiyat Fakultesi Fen Bilimlere Dergisi, 23(2), 2002, 39-43
  4. A. K. Halder and A. C. Paul, Commutativity of two torsion free σ-prime with nonzero derivations, Journal of Physical Sciences, 15 (2011), 27-32
  5. A. K. Halder and A. C. Paul, Jordan left derivations on Lie ideals of Prime Γ-rings, Panjab Univ. Journal of Math., 44 (2012), 23-29
  6. I. N. Herstein, Topic in ring theory, Univ. of Chicago Press, Chicago, 1969
  7. M. F. Hoque and A. C. Paul, On centralizers of semiprime gamma rings, Int. Math. Forum, 6(13) (2011), 627-638
  8. N. Nabusawa, On a generalization of the ring theory, Osaka J. Math., 1 (1964), 65-75
  9. L. Oukhtite, Left derivations on σ-prime rings, Int. J. Algebra, 1 (2007), 31-36
  10. L. Oukhtite and S. Salhi, On commutativity of σ-prime rings. Glas. Mat. Ser. III, 41(1) (2006), 57-64
  11. L. Oukhtite and S. Salhi, On derivations of σ-prime rings, Inter Journal of Algebra, 1(5) (2007), 241-246
  12. L. Oukhtite and S. Salhi, σ-prime rings with a special kind of automorphism, Int. J. Con- temp. Math. Sci., 2(3) (2004), 127-133
  13. A. C. Paul and M. S. Uddin, Lie and Jordan structure in simple Γ-rings, Journal of Physical Sciences, 11 (2010), 77-86
  14. A. C. Paul and M. S. Uddin, Lie structure in simple gamma rings, International Journal of Pure and Applied Sciences and Technology, 4(2) (2010), 63-70
  15. A. C. Paul and M. S. Uddin, Simple gamma rings with involutions, IOSR Journal of Math- ematics, 4(3) (2012), 40-48.