Locally maximal idempotent-generated subsemigroups of singular orientation-preserving transformation semigroups.
type: Item
instance of: scholarly article
title: Locally maximal idempotent-generated subsemigroups of singular orientation-preserving transformation semigroups.
zbMATH Open document ID: 1157.20039
author: B. E. Eshmatov
published in: Semigroup Forum
publication date: 2008-12-02T00:00:00Z
review text: The subject of the paper is the monoid of all orientation-preserving mappings on a finite chain of length \(n\). Most results concern the singular subsemigroup \(SOP_n\) of all non-permutations. It is proved that a set \(A\) of idempotents generates \(SOP_n\) if and only if it contains the set of all increasing, or the set of all decreasing idempotents in the top \(\mathcal J\)-class. The final section characterises what are called the locally maximal idempotent-generated subsemigroups of \(SOP_n\), which are those subsemigroups \(S\) generated by a set of idempotents \(E\) in the maximal \(\mathcal J\)-class of \(SOP_n\) that have the property that the set \(E\) together with any other idempotent \(e\) of the top \(\mathcal J\)-class generates all of \(SOP_n\). These are of two types, one of which consists of the so-called conjugates of the semigroup of all order-preserving mappings on the chain. This allows the authors to also characterise locally maximal idempotent-generated subsemigroups of these conjugates.
reviewed by: Peter M. Higgins
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 5377127
zbMATH Keywords: orientation-preserving transformation semigroups
zbMATH Keywords: maximal idempotent-generated subsemigroups
MaRDI profile type: Publication
full work available at URL: s00233-008-9086-0
OpenAlex ID: W2077206634
cites work: The monoid of orientation-preserving mappings on a chain
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cites work: Products of idempotents of defect 1 in certain semigroups of transformations
cites work: Products of idempotents in finite full transformation semigroups
cites work: Combinatorial results for semigroups of order-preserving mappings
DOI: 10.1007/S00233-008-9086-0
description: scientific article; zbMATH DE number 5377127