Kyungpook Mathematical Journal 2020; 60(4): 683-710
Published online December 31, 2020
Copyright © Kyungpook Mathematical Journal.
Characterizations of Lie Triple Higher Derivations of Triangular Algebras by Local Actions
Let be the set of nonnegative integers and be a 2-torsion free triangular algebra over a commutative ring . In the present paper, under some lenient assumptions on , it is proved that if is a sequence of -linear mappings satisfying for all with (resp. , where p is a nontrivial idempotent of ), then for each , ; where is -linear mapping satisfying for all , i.e. is a higher derivation on and (where is the center of ) is an -linear map vanishing at every second commutator with xy=0 (resp. ).
Keywords: triangular algebra, Lie higher derivation, Lie triple higher derivation