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<p>We extend the notion of chain algebra, originally defined in Gasanova and Nicklasson (J Algebraic Combin 59:473–494, 2024) for finite distributive lattices, to that of finite pure posets. We show this algebra is 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 Gasanova and Nicklasson (2024) 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.</p>

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The chain algebra of a pure poset

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Dancheng Lu

摘要

We extend the notion of chain algebra, originally defined in Gasanova and Nicklasson (J Algebraic Combin 59:473–494, 2024) for finite distributive lattices, to that of finite pure posets. We show this algebra is 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 Gasanova and Nicklasson (2024) 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.