On ideals of Prime Rings with (\sigma, \tau)- Derivations

Authors: Q. DENG, M. Ş. YENİGÜL, N. ARGAÇ

Abstract: Let R be a prime ring. Let \sigma , \tau be two homomorphisms and d be a (\sigma,\tau)-derivation of R. The purpose of this paper is to prove two results: (i) If char R \neq 2, U is a non-zero ideal of R, \sigma is subjective such that \sigma (U) \neq 0, \tau is an automorphism and [d(U), d(U)]_{\sigma,\tau} = 0, then \sigma^2 = \tau^2 and \sigma \tau = \tau \sigma. (ii) Under the assumptions that either char R = 0 or char R > max {2,n}, U is a non-zero right ideal, and \sigma, \tau are automorphisms of R, suppose [d(x),x^n]_{\sigma,\tau} \subseteq C_{\sigma,\tau} for all x \in U, then \sigma = \tau .

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