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Semigroup Forum

, Volume 88, Issue 3, pp 739–752 | Cite as

Schreier split epimorphisms between monoids

  • Dominique Bourn
  • Nelson Martins-Ferreira
  • Andrea Montoli
  • Manuela Sobral
Research Article

Abstract

We explore some properties of Schreier split epimorphisms between monoids, which correspond to monoid actions. In particular, we prove that the split short five lemma holds for monoids, when it is restricted to Schreier split epimorphisms, and that any Schreier reflexive relation is transitive, partially recovering in monoids a classical property of Mal’tsev varieties.

Keywords

Schreier split epimorphisms Monoids Split short five lemma Internal relations 

Notes

Acknowledgments

This work was partially supported by the Centro de Matemática da Universidade de Coimbra (CMUC), funded by the European Regional Development Fund through the program COMPETE and by the Portuguese Government through the FCT - Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0324/2013 and grants number PTDC/MAT/120222/2010 and SFRH/BPD/69661/2010, and also by ESTG and CDRSP from the Polytechnical Institute of Leiria.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Dominique Bourn
    • 1
  • Nelson Martins-Ferreira
    • 2
  • Andrea Montoli
    • 3
  • Manuela Sobral
    • 4
  1. 1.Laboratoire de Mathématiques pures et appliquéesUniversité du Littoral Côte d’OpaleCalaisFrance
  2. 2.ESTG, CDRSPInstituto Politécnico de LeiriaLeiriaPortugal
  3. 3.CMUC, University of CoimbraCoimbraPortugal
  4. 4.CMUC and Department of MathematicsUniversity of CoimbraCoimbraPortugal

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