TY - JOUR

T1 - Some remarks on algebras with straightening laws

AU - Terai, Naoki

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1994/7/25

Y1 - 1994/7/25

N2 - 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.

AB - 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.

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U2 - 10.1016/0022-4049(94)90120-1

DO - 10.1016/0022-4049(94)90120-1

M3 - Article

AN - SCOPUS:43949158425

VL - 95

SP - 87

EP - 101

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 1

ER -