Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

COMMUTATIVITY OF PRIME GAMMA NEAR RINGS WITH GENERALIZED DERIVATIONS

  • MARKOS, ADNEW (Department of Mathematics, College of Natural Sciences, Jimma University) ;
  • MIYAN, PHOOL (Department of Mathematics, College of Natural and Computational Sciences, Haramaya University) ;
  • ALEMAYEHU, GETINET (Department of Mathematics, College of Natural and Computational Sciences, Haramaya University)
  • 투고 : 2021.08.03
  • 심사 : 2022.03.29
  • 발행 : 2022.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The purpose of the present paper is to obtain commutativity of prime Γ-near-ring N with generalized derivations F and G with associated derivations d and h respectively satisfying one of the following conditions:(i) G([x, y]α = ±f(y)α(xoy)βγg(y), (ii) F(x)βG(y) = G(y)βF(x), for all x, y ∈ N, β ∈ Γ (iii) F(u)βG(v) = G(v)βF(u), for all u ∈ U, v ∈ V, β ∈ Γ,(iv) if 0 ≠ F(a) ∈ Z(N) for some a ∈ V such that F(x)αG(y) = G(y)αF(x) for all x ∈ V and y ∈ U, α ∈ Γ.

키워드

참고문헌

  1. A. Ali, H.E. Bell and P. Miyan, Generalized derivations on prime near rings, Inter. J. Math. and Math.Sci. 2013 (2013), Article ID 170749, 5 pages.
  2. A. Ali, H.E. Bell and P. Miyan, Generalized derivations on prime near rings II, Afrika Matematika 26 (2015), 275-282. https://doi.org/10.1007/s13370-013-0205-z
  3. H.E. Bell and G. Mason, On derivations in near-rings, in: Near-rings and Near-Fields, North-Holland Mathematics Studies, 137 (1987), 31-35. https://doi.org/10.1016/S0304-0208(08)72283-7
  4. H.E. Bell, On derivations in near-rings II, in: Near-rings, Near-Fields and K-Loops, Kluwer Academic Publishers, Amsterdam, 1997, 191-197.
  5. Y.U. Cho, and Y.B. Jun, Gamma-derivations in prime and semiprime gamma-near-rings, Indian Journal of Pure and Applied Mathematics 33 (2002), 1489-1494.
  6. J.R. Clay, Nearrings, Geneses and applications, Oxford University Press, 1992.
  7. K.K. Dey, A.C. Paul, and I.S. Rakhimov, On Prime-Gamma-Near-Rings with Generalized Derivations, International Journal of Mathematics and Mathematical Sciences 2012 (2012), Article ID 625968, 14 pages.
  8. M.A. Ibraheem, On commutativity of prime gamma near rings, IOSR Journal of Mathematics 10 (2014), 68-71. https://doi.org/10.9790/5728-10266871
  9. A.A. Kamal, and K.H. Al-Shaalan, Commutativity of rings and near rings with generalized derivations, Indian Journal of Pure and Applied Mathematics 44 (2013), 473-496. https://doi.org/10.1007/s13226-013-0025-8
  10. M. Kazaz, and A. Alkan, Two-sided Γ-α derivations in prime and semiprime Γ-near-rings, Communications of the Korean Mathematical Society 23 (2008), 469-477. https://doi.org/10.4134/CKMS.2008.23.4.469
  11. L. Madhuchelvi, On Generalized derivations in Γ-near rings, International Journal of mathematical sciences and Applications 6 (2016), 89-100.
  12. L. Madhuchelvi, On Generalized derivations in 3-prime Γ-near rings, International Journal of mathematical sciences and Applications 6 (2016), 901-908.
  13. U. Mustafa, M.A. Ozturk, and Y.B. Jun, On prime amma near rings with derivations, Communication Korean Mathematical society 19 (2004), 427-433. https://doi.org/10.4134/CKMS.2004.19.3.427
  14. I.S. Rakhimov, K.K. Dey, and A.C. Paul, Prime Gamma Near Rings with Derivations, International Journal of pure and Applied Mathematics 83 (2013), 221-231.
  15. B. Satyanarayana, Contributions to near ring theory, Doctoral Dissertation, Acharya Nagarjuna University, 1984.
  16. Y.B. Jun, H.K. Kim and Y.U. Cho, On gamma derivations in gamma near rings, Soochow Journal of Mathematics 29 (2003), 275-282.
  17. O. Golbasi, On prime near rings with generalized (α, τ) derivations, Kyungpook Mathematical Journal 45 (2005), 249-249.
  18. Y. Shang, A note on the commutativity of prime near-rings, Algebra Colloquium 22 (2015), 361-366. https://doi.org/10.1142/S1005386715000310