Singular antitone systems
type: Item
instance of: scholarly article
title: Singular antitone systems
zbMATH Open document ID: 0936.06010
DOI: 10.1023/A:1006261921844
author: T. S. Blyth
author: H. J. Silva
published in: Order
publication date: 1999-09-22T00:00:00Z
review text: An antitone system is an ordered set \((P;\leq)\) together with an antitone mapping \(g:P\to P\). Given an ordered set \(P\) and an antitone mapping \(g:P\to P\), the scope of this paper is to give necessary and sufficient conditions for the existence of an odd positive integer \(k\) such that \(g^k\) is isotone. The result obtained has natural applications to the dual space of an Ockham algebra. In particular, the authors determine the cardinality of the endomorphism semigroup of a finite subdirectly irreducible Ockham algebra.
Mathematics Subject Classification ID: 06D30
Mathematics Subject Classification ID: 20M18
zbMATH DE Number: 1340447
zbMATH Keywords: antitone system
zbMATH Keywords: antitone mapping
zbMATH Keywords: Ockham algebra
zbMATH Keywords: endomorphism semigroup
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
full work available at URL: a:1006261921844
OpenAlex ID: W156992964
description: scientific article; zbMATH DE number 1340447