Some remarks on algebras with straightening laws

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Abstract

First in order to investigate deformation of ASLs, we define the moduli space of ASLs on a given poset. And we give an inequality between the depth of general ASLs and that of the corresponding Stanley-Reisner ring, which includes the fundamental theorem on ASLs by De Concini, Eisenbud and Procesi (1982). Secondly we give a counter-example of the following conjecture of Hibi: If there exist an ASL on a finite poset H over a field k which is an integral domain then H is Cohen-Macaulay over k, i.e., the Stanlay-Reisner ring k[H] of H is Cohen-Macaulay.

Original languageEnglish
Pages (from-to)87-101
Number of pages15
JournalJournal of Pure and Applied Algebra
Volume95
Issue number1
DOIs
Publication statusPublished - Jul 25 1994

ASJC Scopus subject areas

  • Algebra and Number Theory

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