Jordan τ-derivations of Prime Rings
Journal
Communications in Algebra
Journal Volume
43
Journal Issue
12
Pages
5195-5204
Date Issued
2015
Author(s)
Lin, J.-H.
Abstract
Let R be a prime ring which is not commutative, with maximal symmetric ring of quotients Qms(R), and let τ be an anti-automorphism of R. An additive map δ: R → Qms(R) is called a Jordan τ-derivation if δ(x2) = δ(x)xτ + xδ(x) for all x ∈ R. A Jordan τ-derivation of R is called X-inner if it is of the form x → axτ − xa for x ∈ R, where a ∈ Qms(R). It is proved that any Jordan τ-derivation of R is X-inner if either R is not a GPI-ring or R is a PI-ring except when charR = 2 and dim CRC = 4, where C is the extended centroid of R.
Type
journal article