Binomial semigroups
type: Item
instance of: scholarly article
title: Binomial semigroups
zbMATH Open document ID: 0910.20038
author: Eric Jespers
author: Jan Okniński
published in: Journal of Algebra
publication date: 1999-04-20T00:00:00Z
review text: A binomial semigroup is a semigroup with a finite set \(x_1,\dots,x_n\) of generators subject to \(\frac{n(n-1)}2\) relations of the type \(x_jx_i=x_kx_l\) with \(j>i\), \(k<l\), \(k<j\). These semigroups were studied by Gateva-Ivanova and Van den Bergh in their investigations of skew polynomial rings. From the authors abstract: ``In this paper we study the structure of binomial semigroups and investigate the height one prime ideals of their binomial skew polynomial rings. In particular, we give a representation theorem of such semigroups as a product of binomial semigroups of fewer generators and we prove that binomial semigroups have (torsion-free) solvable groups of quotients. It is shown that binomial semigroups are Noetherian maximal orders in their quotient group and have trivial normalizing class group. Quotient rings and localizations with respect to height one primes of the binomial skew polynomial ring are described. It follows that binomial skew semigroup rings are Noetherian maximal orders with principal homogeneous height one prime ideals''.
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 1203895
zbMATH Keywords: generators
zbMATH Keywords: relations
zbMATH Keywords: skew polynomial rings
zbMATH Keywords: binomial semigroups
zbMATH Keywords: height one prime ideals
zbMATH Keywords: binomial skew polynomial rings
zbMATH Keywords: groups of quotients
zbMATH Keywords: maximal orders
zbMATH Keywords: localizations
reviewed by: Josif S. Ponizovskii
MaRDI profile type: Publication
full work available at URL: jabr.1997.7292
OpenAlex ID: W4213329577
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DOI: 10.1006/JABR.1997.7292
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description: scientific article; zbMATH DE number 1203895