Bi-Lie n-derivations on triangular rings

Abstract

The purpose of this article is to prove that every bi-Lie n-derivation of certain triangular rings is the sum of an inner biderivation, an extremal biderivation and an additive central mapping vanishing at $ (n-1)^{th} $-commutators for both components, using the notion of maximal left ring of quotients. As a consequence, we characterize the decomposition structure of bi-Lie n-derivations on upper triangular matrix rings.

Keywords

• triangular rings
• upper triangular matrix rings
• extremal biderivation
• maximal left ring of quotients
• bi-lie n-derivation