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On the discrete counterparts of Cohen-Macaulay algebras with straightening laws

Mitsuhiro Miyazaki
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Abstract

We study properties of a poset generating a Cohen-Macaulay algebra with straightening laws (ASL for short). We show that if a poset $P$ generates a Cohen-Macaulay ASL, then $P$ is pure and, if $P$ is moreover Buchsbaum, then $P$ is Cohen-Macaulay. Some results concerning a Rees algebra of an ASL defined by a straightening closed ideal are also established. And it is shown that if $P$ is a Cohen-Macaulay poset with unique minimal element and $Q$ is a poset ideal of $P$, then $P\uplus Q$ is also Cohen-Macaulay.

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Mitsuhiro Miyazaki. 2004-10-10. On the discrete counterparts of Cohen-Macaulay algebras with straightening laws. https://arxiv.org/abs/math/0410253

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