NONLINEAR JORDAN HIGHER DERIVATIONS ON TRIANGULAR RINGS

Year 2014, Volume: 15 Issue: 15, 56 - 65, 01.06.2014

Chunhui Xue Runling An Huiyuan Zhang

https://doi.org/10.24330/ieja.266237

Cited By: 1

Abstract

Let T be a triangular ring. We say that a family of maps δ ={δn, δn : T → T , n ∈ N} is a Jordan higher derivable map (without assumption
of additivity or continuity) if δn(AB + BA) = Pi+j=n[δi(A)δj (B) +δj (B)δi(A)] for all A, B ∈ T . In this paper, we show that every Jordan higher
derivable map on a triangular ring is a higher derivation. As its application, we
get that every Jordan higher derivable map on an irreducible CDCSL algebra
or a nest algebra is a higher derivation, and new characterizations of higher
derivations on these algebras are obtained.

Keywords

Higher derivation, triangular rings, CDCSL algebras