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

Güven E., Soytürk M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.36, ss.19-25, 2007 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36
  • Basım Tarihi: 2007
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.19-25
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.