Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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A NOTE ON GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS

  • RAZA, MOHD ARIF (Department of Mathematics, Faculty of Science & Arts-Rabigh, King Abdulaziz University) ;
  • REHMAN, NADEEM UR (Department of Mathematics, Aligarh Muslim University) ;
  • GOTMARE, A.R. (GDM Arts, KRN Commerce and MD Science Colledge)
  • 투고 : 2020.05.14
  • 심사 : 2020.10.16
  • 발행 : 2021.01.30
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초록

Let R be a prime ring, Qr be the right Martindale quotient ring and C be the extended centroid of R. If �� be a nonzero generalized skew derivation of R and f(x1, x2, ⋯, xn) be a multilinear polynomial over C such that (��(f(x1, x2, ⋯, xn)) - f(x1, x2, ⋯, xn)) ∈ C for all x1, x2, ⋯, xn ∈ R, then either f(x1, x2, ⋯, xn) is central valued on R or R satisfies the standard identity s4(x1, x2, x3, x4).

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