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On divisors of semigroups of order-preserving mappings of a finite chain

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Abstract

We show that if a semigroup T divides a semigroup of full order preserving transformations of a finite chain, then so does any semidirect product S⋊T where S is a finite semilattice whose natural order makes S a chain.

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Authors and Affiliations

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

    V. H. Fernandes

  2. CAUL, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    V. H. Fernandes

  3. Department of Mathematics and Mechanics, Ural State University, Lenina 51, 620083, Ekaterinburg, Russia

    M. V. Volkov

Authors
  1. V. H. Fernandes
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  2. M. V. Volkov
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Correspondence to V. H. Fernandes.

Additional information

Communicated by Jorge Almeida.

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Fernandes, V.H., Volkov, M.V. On divisors of semigroups of order-preserving mappings of a finite chain. Semigroup Forum 81, 551–554 (2010). https://doi.org/10.1007/s00233-010-9257-7

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  • DOI: https://doi.org/10.1007/s00233-010-9257-7

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