On monomial algebras
type: Item
instance of: scholarly article
title: On monomial algebras
zbMATH Open document ID: 0627.20042
DOI: 10.1007/BF01196501
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: Let X be a finitely generated free semigroup and let I be an ideal of X. The structure and properties of the contracted semigroup ring K[X/I] of the Rees factor semigroup X/I over a field K are investigated. Among other things, the Jacobson radical and the chain conditions for K[X/I] are discussed. The main result shows that K[X/I] is a PI-algebra if and only if X/I satisfies a permutational property, that is there exists \(n\geq 2\) such that for any \(a_ 1,...,a_ n\in X/I\) there is a nontrivial permutation \(\sigma\) with \(a_ 1...a_ n=a_{\sigma (1)}...a_{\sigma (n)}\).
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 16Rxx
Mathematics Subject Classification ID: 16Nxx
zbMATH DE Number: 4019343
zbMATH Keywords: finitely generated free semigroup
zbMATH Keywords: ideal
zbMATH Keywords: contracted semigroup ring
zbMATH Keywords: Rees factor semigroup
zbMATH Keywords: Jacobson radical
zbMATH Keywords: chain conditions
zbMATH Keywords: PI-algebra
zbMATH Keywords: permutational property
author: Jan Okniński
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01196501
OpenAlex ID: W2082488725
description: scientific article; zbMATH DE number 4019343