Semigroups of order-decreasing graph endomorphisms
type: Item
instance of: scholarly article
title: Semigroups of order-decreasing graph endomorphisms
zbMATH Open document ID: 0916.20043
published in: Semigroup Forum
publication date: 1999-07-20T00:00:00Z
review text: This paper studies the varieties (meaning here pseudovarieties of finite semigroups) and languages generated by semigroups of order-decreasing graph endomorphisms on a (finite) poset. Links with related conditions are also investigated: for instance, a mapping is a graph endomorphism on a chain with loops at each point if and only if it is a contraction mapping. Some sample results are that the variety \(GE\) generated by all semigroups of order-decreasing graph endomorphisms on a chain equals \(MK\), the variety generated by the monoids \(S^1\), where \(S\in K\), the variety of semigroups whose idempotents are left zeros. The class of \(\mathcal R\)-trivial semigroups that have the property that left multiplication by an idempotent is a homomorphism is a variety strictly containing \(GE\) (though both varieties have the same monoids) but strictly contained in the variety generated by partial order-decreasing mappings on a chain which, in turn, is a proper subvariety of \(\mathcal R\)-trivial semigroups. The languages corresponding to the variety \(GE\) are explicitly described.
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20M35
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1251284
zbMATH Keywords: pseudovarieties of finite semigroups
zbMATH Keywords: semigroups of order-decreasing graph endomorphisms
zbMATH Keywords: \(\mathcal R\)-trivial semigroups
zbMATH Keywords: partial order-decreasing mappings
zbMATH Keywords: languages
author: A. S. Vernitskiĭ
reviewed by: Peter M. Higgins
MaRDI profile type: Publication
full work available at URL: s002339900016
OpenAlex ID: W2042377140
DOI: 10.1007/S002339900016
description: scientific article; zbMATH DE number 1251284