The lattice of \(\mathcal J\)-classes of \(({\mathcal J},\sigma)\)-irreducible monoids. II
type: Item
instance of: scholarly article
title: The lattice of \(\mathcal J\)-classes of \(({\mathcal J},\sigma)\)-irreducible monoids. II
zbMATH Open document ID: 0940.20066
author: Zhuo Li
published in: Journal of Algebra
publication date: 2000-07-17T00:00:00Z
review text: An algebraic monoid \(M\) is called reductive if its unit group \(G\) is a reductive group. The paper is concerned with \(({\mathcal J},\sigma)\)-irreducible monoids, introduced by the author and \textit{L. E. Renner} [in part I, J. Algebra 190, No. 1, 172-194 (1997; Zbl 0879.20035)]. This is a class properly containing \(\mathcal J\)-irreducible monoids. For the latter class, a general structure theorem for the lattice of \(\mathcal J\)-classes was obtained by \textit{M. S. Putcha} and \textit{L. E. Renner} [in J. Algebra 116, No. 2, 385-399 (1988; Zbl 0678.20039)]. In the paper review, the lattice of \(\mathcal J\)-classes of \(M\) is described if \(M\) is \(({\mathcal J},\sigma)\)-irreducible and the group \(G\) is of type \(D^2_n\) or \(A_n\), \(n\leq 3\).
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 1384441
zbMATH Keywords: Dynkin diagrams
zbMATH Keywords: \(({\mathcal J},\sigma)\)-irreducible monoids
zbMATH Keywords: lattices of \(\mathcal J\)-classes
zbMATH Keywords: algebraic monoids
zbMATH Keywords: unit groups
zbMATH Keywords: reductive groups
reviewed by: Jan Okniński
MaRDI profile type: Publication
full work available at URL: jabr.1999.7947
OpenAlex ID: W1963986233
cites work: Q5662096
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DOI: 10.1006/JABR.1999.7947
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description: scientific article; zbMATH DE number 1384441