Study of three-dimensional algebras with straightening laws which are Gorenstein domains. III
type: Item
instance of: scholarly article
title: Study of three-dimensional algebras with straightening laws which are Gorenstein domains. III
zbMATH Open document ID: 0656.13024
author: Takayuki Hibi
published in: Hiroshima Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let k be a field, A a polynomial ring in a finite number of indeterminates over k and H a poset with an injection \(\rho:\quad H\to A\) such that \(\rho\) (H) is a set of monomials of A. Then (H,\(\rho)\) is called a toroidal poset, provided \(R_{\rho}=k[\rho (H)]\) is a homogeneous algebra with straightening laws. (H,\(\rho)\) is called Gorenstein, if \(R_{\rho}\) is a Gorenstein ring. Continuing part I and II of this paper [see the author's joint work with \textit{K. Watanabe}, Hiroshima Math. J. 15, 27-54, 321-340 (1985; Zbl 0633.13003 and 13004)] the author gives a classification of Gorenstein toroidal posets (H,\(\rho)\) with \(\dim (R_{\rho})=3\) up to equivalence (see loc. cit.). This is done by the help of certain combinatorial information about posets from a ring theoretical property of an affine semigroup ring given by the author in Nagoya Math. J. 112, 1-24 (1988; Zbl 0627.13001).
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 14M05
zbMATH DE Number: 4071068
zbMATH Keywords: algebra with straightening laws
zbMATH Keywords: Gorenstein toroidal posets
reviewed by: Peter Schenzel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206129725
OpenAlex ID: W4233169875
DOI: 10.32917/HMJ/1206129725
description: scientific article; zbMATH DE number 4071068