| In this paper,we study nonlinear higher derivable maps related to idempotents and square zero elements on triangular algebras.The following is the main contents:In Chapter 1,we introduce some common symbols and definitions（for example,triangular algebra and higher derivation）which will be used in this paper.In Chapter 2,we study a class of higher derivable nonlinear maps related to idempotents.Let T=Tri（A,M,B）be a triangular algebra,and ｛δn｝n∈N:T→T be a family of maps（without the assumption of additivity and where δ0 is the identity map）.If ｛δn}n∈N satisfies（?）for any U,V ∈ T and at least one of them is an idempotent,then {δn｝n∈N is an additive higher derivation on T.In Chapter 3,we study nonlinear maps which are ξ-Lie higher derivable by Lie product square zero elements on triangular algebras.Let T=Tri（A,M,B）be a 2-torsion free triangular algebra,S={S ∈T:S2=0} be the set of square zero elements on T and {Φn}n∈NN:T→T be a family of maps（without the assumption of additivity and where Φ0 is the identity map）.If {Φn}n∈N satisfies（?）（?）for any W,X ∈T and[W,X]∈S,then ｛Φn}n∈N is an additive higher derivation on T. |
