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Semigroup Forum

, Volume 54, Issue 1, pp 230–236 | Cite as

Semigroups of order preserving mappings on a finite chain: A new class of divisors

  • Vitor H. Fernandes
Research Article

Abstract

In this paper we aim to prove that every semigroup of the pseudovariety generated by all semigroups of partial, injective and order preserving transformations on a finite chain belongs to the pseudovariety generated by all semigroups of order preserving mappings on a finite chain.

Keywords

Inverse Semigroup Regular Semigroup Order Preserve Partial Transformation Injective Morphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Higgins, Peter M.,Divisors of semigroups of order preserving mappings on a finite chain, Tech. Report No. 94-4, Univ. of Essex (to appear in Int. J. Algebra and Computation).Google Scholar
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    Higgins, Peter M.,Random products in semigroups of mappings, Lattices, Semigroups, and Universal Algebra, Plenum Press, New York, 1990.Google Scholar
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    Pin, J.-E.,Varieties of Formal Languages, North Oxford Academic, 1986.Google Scholar
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    Vernitskii, A. S., and M. V. Volkov,A proof and a generalisation of Higgins’ division theorem for semigroups of order preserving mappings, Izv.vuzov. Matematika, 1995, No. 1, 38–44.Google Scholar

Copyright information

© By Springer-Verlag New York Inc. 1997

Authors and Affiliations

  • Vitor H. Fernandes
    • 1
  1. 1.Departamento de Matemática Faculdade de Ciências e TecnologiaUniversidade Nova de Lisboa Quinta da TorrePortugal

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