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Semigroup Forum

, Volume 81, Issue 2, pp 277–285 | Cite as

Endomorphisms of the semigroup of order-preserving mappings

  • V. H. Fernandes
  • M. M. Jesus
  • V. Maltcev
  • J. D. Mitchell
Research Article

Abstract

We characterize the endomorphisms of the semigroup of all order-preserving mappings on a finite chain. We show that there are three types of endomorphism: automorphisms, constants, and a certain type of endomorphism with two idempotents in the image.

Keywords

Endomorphisms Semigroups Order-preserving mappings 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • V. H. Fernandes
    • 1
    • 2
  • M. M. Jesus
    • 1
    • 2
  • V. Maltcev
    • 3
  • J. D. Mitchell
    • 3
  1. 1.Departamento de Matematica, Faculdade de Ciencias e TecnologiaUniversidade Nova de LisboaMonte da CaparicaPortugal
  2. 2.Centro de Algebra da Universidade de LisboaLisboaPortugal
  3. 3.Mathematical InstituteFifeUK

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