Fixed points of endomorphisms of trace monoids.
type: Item
instance of: scholarly article
title: Fixed points of endomorphisms of trace monoids.
zbMATH Open document ID: 1309.20052
author: Emanuele Rodaro
author: Pedro V. Silva
published in: Semigroup Forum
publication date: 2014-11-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1211.4517
review text: Given an alphabet \(A\) and a symmetric anti-reflexive relation \(I\) on \(A\), the corresponding \textit{trace monoid} is given by presentation \(\langle A:ab=ba,\;(a,b)\in I\rangle\). In the paper under review it is shown that the fixed point submonoid and the periodic point submonoid associated to an endomorphism of a trace monoid over a finite alphabet are always finitely generated. The second main result of the paper addresses the question of rationality for fixed point monoids. It is shown that rationality for all endomorphisms is equivalent to the requirement for the original trace monoid to be a free product of free commutative monoids.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M35
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 68Q45
zbMATH DE Number: 6363670
zbMATH Keywords: trace monoids
zbMATH Keywords: finitely generated monoids
zbMATH Keywords: endomorphisms
zbMATH Keywords: fixed points
zbMATH Keywords: transitive forests
zbMATH Keywords: free products
zbMATH Keywords: periodic points
MaRDI profile type: Publication
OpenAlex ID: W1976559603
arXiv ID: 1211.4517
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DOI: 10.1007/S00233-013-9553-0
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description: scientific article; zbMATH DE number 6363670