Commuting maps on certain incidence algebras

Abstract

Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected components, in this paper we give a sufficient and necessary condition for each commuting map on $I(X,\mathcal{R})$ being proper.

9 pages, first version, comments welcome. arXiv admin note: text overlap with arXiv:1901.05690; text overlap with arXiv:1608.00110 by other authors