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The chain algebra of a pure poset

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arxiv 2410.05024 v4 pith:RBOAN2HO submitted 2024-10-07 math.CO math.AC

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keywords algebrachainpolytopepureciteextendfinitegorenstein
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We extend the notion of chain algebra, originally defined in \cite{GN} for finite distributive lattices, to that of finite pure posets. We show this algebra corresponds to the Ehrhart ring of a (0,1)-polytope, termed the chain polytope, and characterize the indecomposability of this polytope. Furthermore, we prove the normality of the chain algebra, describe its canonical module, and extend one of main results from \cite{GN} by computing its Krull dimension. For width-2 pure posets, we determine the algebra's regularity and conditions for it to be Gorenstein or nearly Gorenstein.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. When do pseudo-Gorenstein rings become Gorenstein?

    math.AC 2025-02 conditional novelty 6.0 of 10

    A pseudo-Gorenstein graded ring becomes Gorenstein when the trace ideal of its canonical module contains a length-two regular sequence in the initial degree, with applications to nearly and almost Gorenstein rings.

  2. The canonical trace of Stanley-Reisner rings that are Gorenstein on the punctured spectrum

    math.AC 2024-12 conditional novelty 6.0 of 10

    Nearly Gorenstein Stanley-Reisner rings of dimension at least three are Gorenstein, and canonical traces of punctured-Gorenstein Stanley-Reisner rings are exactly the ring, the maximal ideal, or its square.

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