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arXiv · 2412.18049

Additive Biderivations of Incidence Algebras

Zhipeng Guan·Chi Zhang
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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.

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Zhipeng Guan, Chi Zhang. 2024-12-23. Additive Biderivations of Incidence Algebras. https://arxiv.org/abs/2412.18049

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