Notes on Traces of a Symmetric Generalized (σ, τ)-Biderivations and Commutativity in Prime Rings

Abstract

Let R be a 2-torision free prime ring and σ, τ∈ Aut(R). Furthermore, G: R×R→R is a symmetric generalized (σ, τ)-Biderivation associated with a nonzero (σ, τ)-Biderivation D. In this paper some certain identities are presented satisfying by the traces of G and D on an ideal of R which forces R to be commutative.