Some Results on (σ,τ)-Left Jordan Ideals in Prime Rings

Abstract

In this paper we have proved the following results. Let R be a prime ring,U be (σ,τ)-left Joradan ideal of R where σ,τ: R→R be two automorphisms of R and d be a nonzero derivation of R . (1) If (R,a)σ,τ=0, then aZ(R). (2) If aU=0(or Ua=0) and aR , then a=0 or UZ(R). (3) If characteristic of R not equal 2 and U Cσ,τ, then σ(u)+τ(u)Z(R) for all uU.(4) If d(U)=0, dτ=τd and dσ=σd , then σ(u)+τ(u)Z(R) for all uU.