Additive Biderivations of Incidence Algebras

Abstract

Let $\mathcal{R}$ be a commutative ring with unity, and let $P$ be a locally finite poset. The aim of the paper is to provide an explicit description of the additive biderivations of the incidence algebra $I(P, \mathcal{R})$. We demonstrate that every additive biderivation is the sum of several inner biderivations and extremal biderivations. Furthermore, if the number of elements in any maximal chain in $P$ is infinite, every additive biderivation of $I(P,\mathcal{R})$ is the sum of several inner biderivations.