SOME RESULTS ON PRIME RINGS AND (sigma, tau) - LIE IDEALS


Güven E. , Soytürk M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.36, pp.19-25, 2007 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 36
  • Publication Date: 2007
  • Title of Journal : HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Page Numbers: pp.19-25

Abstract

Let R be a prime ring with characteristic not 2, sigma, tau, alpha, beta, lambda, mu are automorphisms of R and d : R -> R a nonzero (sigma, tau)-derivation. Suppose that a epsilon R. In this paper, we give some results on (sigma, tau)-Lie ideals and prove that, (1) If [a, d(R)](alpha,beta) = 0 and d sigma = sigma d, d tau = tau d, then a epsilon C-alpha,C-beta. (2) Let d(1) be a nonzero (sigma,tau)-derivation and d(2) an (alpha,beta)-derivation of R such that d(2)a = alpha d(2), d(2)beta = beta d(2). If [d(1)(R),d(2)(R)](lambda,mu) = 0 then R is commutative. (3) If I is a nonzero ideal of R and d(x, y) = 0 for all x, y epsilon I, then R is commutative. (4) If d(R, a) = 0 then (d(R), a)(sigma,tau) = 0.