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Indecomposable Ideals in Incidence Algebras

Rafael D. Sorkin
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Abstract

The elements of a finite partial order $P$ can be identified with the maximal indecomposable two-sided ideals of its incidence algebra $\A$, and then for two such ideals, $I\prec J \iff IJ \not=0$. This offers one way to recover a poset from its incidence algebra. In the course of proving the above, we classify all of the two-sided ideals of $\A$.

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BibTeXRIS

Rafael D. Sorkin. 2003-09-07. Indecomposable Ideals in Incidence Algebras. https://doi.org/10.1142/s0217732303012738

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