ON MULTIPLICATIVE LIE n-HIGHER DERIVATIONS OF TRIANGULAR ALGEBRAS

Let $\mathrm{R}$ be a commutative ring with unity, $\mathrm{A},\mathrm{B}$ be $\mathrm{R}$-algebras and $\mathrm{M}$ be an $(\mathrm{A}, \mathrm{B})$-bimodule. Let $\mathfrak{T}=Tri(\mathrm{A},\mathrm{M},\mathrm{B})$ be a $(n-1)$-torsion free triangular algebra. In this article, we prove that every multiplicative Lie $n$-higher derivation on triangular algebras has the standard form. Also, the main result is applied to some classical examples of triangular algebras such as upper triangular matrix algebras and nest algebras