On semigroups of endomorphisms of a chain with restricted range.
type: Item
instance of: scholarly article
title: On semigroups of endomorphisms of a chain with restricted range.
zbMATH Open document ID: 1309.20051
author: Preeyanuch Honyam
author: Teresa M. Quinteiro
author: Boorapa Singha
author: Vítor H. Fernandes
published in: Semigroup Forum
publication date: 2014-11-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1306.2774
review text: For a (possibly infinite) chain \(X\) and a non-empty subset \(Y\) of \(X\) the paper under review studies the semigroup \(O(X,Y)\) of all endomorphisms of \(X\) whose image is contained in \(Y\). The main result of the paper characterizes Green's relations for and characterizes the largest regular subsemigroup in \(O(X,Y)\). For finite chains the authors also classify semigroups \(O(X,Y)\) up to isomorphism and determine their rank.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M20
zbMATH DE Number: 6363659
zbMATH Keywords: transformation semigroups
zbMATH Keywords: chains
zbMATH Keywords: ranks
zbMATH Keywords: endomorphisms with restricted range
zbMATH Keywords: Green relations
zbMATH Keywords: regular semigroups
MaRDI profile type: Publication
OpenAlex ID: W1992493192
arXiv ID: 1306.2774
cites work: Posets whose monoids of order-preserving maps are regular
cites work: Q5721233
cites work: Q5610412
cites work: The Gap Between Partial and Full
cites work: Semigroups of order preserving mappings on a finite chain: A new class of divisors
cites work: On the Ranks of Semigroups of Transformations on a Finite Set with Restricted Range
cites work: On divisors of semigroups of order-preserving mappings of a finite chain.
cites work: Endomorphisms of the semigroup of order-preserving mappings.
cites work: On the ranks of certain semigroups of order-preserving transformations
cites work: Q5592263
cites work: DIVISORS OF SEMIGROUPS OF ORDER-PRESERVING MAPPINGS ON A FINITE CHAIN
cites work: Products of idempotents in certain semigroups of transformations
cites work: Q4846425
cites work: Regular order-preserving transformation semigroups
cites work: Regularity conditions for semigroups of isotone transformations of countable chains.
cites work: THE IDEAL STRUCTURE OF SEMIGROUPS OF TRANSFORMATIONS WITH RESTRICTED RANGE
cites work: Q3009676
cites work: Q3428803
cites work: Semigroups of order-preserving mappings
cites work: The finite basis problem for pseudovariety
cites work: Regularity and Green's relations on a semigroup of transformations with restricted range.
cites work: Maximal and minimal congruences on some semigroups.
cites work: SEMIGROUPS OF LINEAR TRANSFORMATIONS WITH RESTRICTED RANGE
cites work: Some results concerning a transformation semigroup
DOI: 10.1007/S00233-013-9548-X
description: scientific article; zbMATH DE number 6363659