Automorphisms and products of ordered sets
type: Item
instance of: scholarly article
title: Automorphisms and products of ordered sets
zbMATH Open document ID: 0554.06004
DOI: 10.1007/BF01201105
author: Dwight Duffus
published in: Algebra Universalis
publication date: 1984-01-01T00:00:00Z
review text: An ordered set X has the fixed point property if every order preserving map of X to X has a fixed point. The paper deals with the following problem: if ordered sets X and Y have the fixed point property, does it follow that the (cardinal) product XY has the fixed point property. The main result is the following. Let X and Y be both either finite connected ordered sets or connected ordered sets, each with a decomposition as a product of product indecomposable ordered sets. Then XY has a fixed point free automorphism if and only if at least one of X and Y has a fixed point free automorphism.
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 3882493
zbMATH Keywords: fixed point property
zbMATH Keywords: connected ordered sets
zbMATH Keywords: product of product indecomposable ordered sets
zbMATH Keywords: fixed point free automorphism
reviewed by: V. Yu. Meskhi
MaRDI profile type: Publication
cites work: Fixed points in partially ordered sets
cites work: Refinement properties for relational structures
cites work: A Logarithmic Property for Exponents of Partially Ordered Sets
cites work: Retracts and the Fixed Point Problem for Finite Partially Ordered Sets
cites work: On direct product desomposition of partially ordered sets
cites work: Q3964624
cites work: Graph multiplication
cites work: Isotone relations and the fixed point property for posets
full work available at URL: https://doi.org/10.1007/bf01201105
OpenAlex ID: W1995184902
description: scientific article; zbMATH DE number 3882493