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

2004/10/10 by Mitsuhiro Miyazaki, Miyazaki, Mitsuhiro
Mathematics · #13C15 #13F50 #13F55 #13H10 #13P10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C15 #msc:13F50 #msc:13F55 #msc:13H10 #msc:13P10

paper · pdf · doi:10.48550/arxiv.math/0410253

arxiv created 2004/10/10 · arxiv updated 2009/12/01

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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