Lie Derivations of Incidence Algebras

Abstract

Let $X$ be a locally finite preordered set, $\mathcal{R}$ a commutative ring with identity and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. In this note we prove that each Lie derivation of $I(X,\mathcal{R})$ is proper, provided that $\mathcal{R}$ is $2$-torsion free.

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