Abstract
The elements of a finite partial order P can be identified with the maximal indecomposable two-sided ideals of its incidence algebra [Formula: see text], and then for two such ideals, I ≺ J ⇔ IJ ≠ 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 [Formula: see text].
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