Order-preserving transformations with restricted range: regularity, Green's relations, and ideals.
type: Item
instance of: scholarly article
title: Order-preserving transformations with restricted range: regularity, Green's relations, and ideals.
zbMATH Open document ID: 1332.20064
author: Worachead Sommanee
author: Jintana Sanwong
published in: Algebra Universalis
publication date: 2015-10-14T00:00:00Z
review text: The paper studies the subsemigroup of the semigroup of all order-preserving transformations of a linearly ordered set \(X\) which consists of all transformations \(\alpha\) whose image belongs to a fixed subset \(Y\) of \(X\) and, additionally, satisfies \(\alpha(X)=\alpha(Y)\). The authors characterize regular elements in this subsemigroup, describe Green's relations and characterize ideals. As an application, the authors show that this semigroup is idempotent generated.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M20
zbMATH DE Number: 6494311
zbMATH Keywords: semigroups of order-preserving transformations
zbMATH Keywords: Green relations
zbMATH Keywords: ideals
zbMATH Keywords: regular elements
zbMATH Keywords: idempotent generated subsemigroups
MaRDI profile type: Publication
full work available at URL: s00012-015-0354-z
OpenAlex ID: W1144496853
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DOI: 10.1007/S00012-015-0354-Z
description: scientific article; zbMATH DE number 6494311