Infinite iteration of matrix semigroups. I: Structure theorem for torsion semigroups
type: Item
instance of: scholarly article
title: Infinite iteration of matrix semigroups. I: Structure theorem for torsion semigroups
zbMATH Open document ID: 0584.20053
DOI: 10.1016/0021-8693(86)90005-0
author: B. George
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: The main result of this paper is a representation theorem for countable torsion monoids, that is, countable monoids in which every element is of finite order. Every such monoid T is the homomorphic image \(\sigma\) (S) of a torsion monoid S with S and \(\sigma\) having several special properties some of which can be roughly described as follows: S is obtained by an infinitely iterated sandwich matrix type of construction based on certain cyclic submonoids of T and on translations of finite subsets of T. The morphism \(\sigma\) is of a restricted kind, defined along with the matrix construction. The maximal subgroups of S are finite cyclic groups and the restriction of \(\sigma\) to these is injective. S can be characterized as an elementary projective limit of finitely iterated matrix semigroups.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M15
Mathematics Subject Classification ID: 20M30
zbMATH DE Number: 3935334
zbMATH Keywords: representation theorem
zbMATH Keywords: countable torsion monoids
zbMATH Keywords: sandwich matrix
zbMATH Keywords: projective limit of finitely iterated matrix semigroups
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90005-0
OpenAlex ID: W2020235161
cites work: Q5564342
cites work: Q4132170
cites work: Q5570933
cites work: Q3853827
description: scientific article; zbMATH DE number 3935334