A note on generators of the endomorphism semigroup of an infinite countable chain-Reference-Cited by-同舟云学术

A note on generators of the endomorphism semigroup of an infinite countable chain

Published:2017-02 Issue:02 Volume:16 Page:1750031
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Dimitrova Ilinka¹,Fernandes Vítor H.²,Koppitz Jörg³

Affiliation:

1. Faculty of Mathematics and Natural Science, South-West University “Neofit Rilski”, 2700 Blagoevgrad, Bulgaria

2. CMA, Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, Monte da Caparica, 2829516 Caparica, Portugal

3. Institute of Mathematics, University of Potsdam, 14476 Potsdam, Germany

Abstract

In this note, we consider the semigroup [Formula: see text] of all order endomorphisms of an infinite chain [Formula: see text] and the subset [Formula: see text] of [Formula: see text] of all transformations [Formula: see text] such that [Formula: see text]. For an infinite countable chain [Formula: see text], we give a necessary and sufficient condition on [Formula: see text] for [Formula: see text] to hold. We also present a sufficient condition on [Formula: see text] for [Formula: see text] to hold, for an arbitrary infinite chain [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498817500311

Reference8 articles.

1. Posets whose monoids of order-preserving maps are regular

2. On semigroups of endomorphisms of a chain with restricted range

3. GENERATING THE FULL TRANSFORMATION SEMIGROUP USING ORDER PRESERVING MAPPINGS

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