ON GENERALIZED (σ, τ)-BIDERIVATIONS IN RINGS

Abstract

Let σ, τ be automorphisms of a ring R. In the present paper many concepts related to biadditive mappings of rings, viz. σ-left centralizer traces, symmetric generalized (σ, τ)-biderivations, σ-left bimultipliers and symmetric generalized Jordan (σ, τ)-biderivations are studied. Many results related to these concepts are given. It is established that every symmetric generalized (σ, τ)-biderivation of a prime ring of characteristic different from 2, can be reduced to a σ-left bimultiplier under certain algebraic conditions. Further, it is shown that every symmetric generalized Jordan (σ, τ)-biderivation of a prime ring of characteristic different from 2 is a symmetric generalized (σ, τ)-biderivation.