Lie higher derivations of arbitrary triangular algebras

TL;DR

This paper investigates Lie higher derivations on arbitrary triangular algebras, demonstrating that all such derivations are proper by utilizing maximal ring of quotients, thus extending previous results in the field.

Contribution

It establishes that every Lie higher derivation on an arbitrary triangular algebra is proper, generalizing prior work and employing the concept of maximal ring of quotients.

Findings

All Lie higher derivations are proper on arbitrary triangular algebras.

Utilizes maximal ring of quotients to prove the main result.

Extends previous results on Lie derivations in algebra.

Abstract

Motivated by the works of Wang [Y. Wang, \textit{Lie (Jordan) derivations of arbitrary triangular algebras,} Aequationes Mathematicae, \textbf{93} (2019), 1221-1229] and Moafian et al. [F. Moafian and H. R. Ebrahimi Vishki, \textit{Lie higher derivations on triangular algebras revisited,} Filomat, \textbf{30}(12) (2016), 3187-3194.], we shall study Lie higher derivations of arbitrary triangular algebras. In fact, it is shown that every Lie higher derivation on an arbitrary triangular algebra is proper, using the notion of maximal left (right) ring of quotients.