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Endomorphisms of the semigroup of order-preserving mappings

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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.

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Authors and Affiliations

  1. Departamento de Matematica, Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, 2829-516, Monte da Caparica, Portugal

    V. H. Fernandes & M. M. Jesus

  2. Centro de Algebra da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003, Lisboa, Portugal

    V. H. Fernandes & M. M. Jesus

  3. Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, UK

    V. Maltcev & J. D. Mitchell

Authors
  1. V. H. Fernandes
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  2. M. M. Jesus
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  3. V. Maltcev
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  4. J. D. Mitchell
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Corresponding author

Correspondence to J. D. Mitchell.

Additional information

Communicated by Norman R. Reilly.

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Fernandes, V.H., Jesus, M.M., Maltcev, V. et al. Endomorphisms of the semigroup of order-preserving mappings. Semigroup Forum 81, 277–285 (2010). https://doi.org/10.1007/s00233-010-9220-7

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  • DOI: https://doi.org/10.1007/s00233-010-9220-7

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