Lie-type derivations of finitary incidence algebras

Abstract

Let $P$ be an arbitrary partially ordered set, $R$ be a commutative ring with identity and $FI\left(P,R\right)$ be the finitary incidence algebra of $P$ over $R$. Under some natural assumption on $R$, we prove that each Lie-type derivation of $FI\left(P,R\right)$ is proper, which partially generalizes the main results of Zhang and Khrypchenko (2017), Wang and Xiao (2019), and Xiao and Yang (2019).