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Shellability of semigroup rings

Published online by Cambridge University Press:  22 January 2016

Annetta Aramova ,
Jürgen Herzog  and
Takayuki Hibi
Annetta Aramova
Affiliation:
FB6 Mathematik und Informatik, Universität – GHS – Essen, Postfach 103764, 45117 Essen, Germany, A.Aramova@uni-essen.de
Jürgen Herzog
Affiliation:
FB6 Mathematik und Informatik, Universität – GHS – Essen, Postfach 103764, 45117 Essen, Germany, juergen.herzog@uni-essen.de
Takayuki Hibi
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan, hibi@math.sci.osaka-u.ac.jp
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Abstract

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The concepts of Λ-shellability of locally finite posets as well as of extendable sequentially Koszul algebras will be introduced. It will be proved that the divisor poset of a homogeneous semigroup ring is Λ-shellable if and only if the semigroup ring is extendable sequentially Koszul. Examples of extendable sequentially Koszul semigroup rings contain all monomial ASL’s (algebras with straightening laws) and all second squarefree Veronese subrings.

Keywords

13H1013F5013F55
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 168 , 2002 , pp. 65 - 84
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

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