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Schreier split epimorphisms between monoids

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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.

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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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Authors and Affiliations

  1. Laboratoire de Mathématiques pures et appliquées, Université du Littoral Côte d’Opale, Calais, France

    Dominique Bourn

  2. ESTG, CDRSP, Instituto Politécnico de Leiria, Leiria, Portugal

    Nelson Martins-Ferreira

  3. CMUC, University of Coimbra, 3001-454 , Coimbra, Portugal

    Andrea Montoli

  4. CMUC and Department of Mathematics, University of Coimbra, 3001-454 , Coimbra, Portugal

    Manuela Sobral

Authors
  1. Dominique Bourn
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  2. Nelson Martins-Ferreira
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  3. Andrea Montoli
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  4. Manuela Sobral
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Corresponding author

Correspondence to Andrea Montoli.

Additional information

Communicated by László Márki.

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Bourn, D., Martins-Ferreira, N., Montoli, A. et al. Schreier split epimorphisms between monoids. Semigroup Forum 88, 739–752 (2014). https://doi.org/10.1007/s00233-014-9571-6

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  • DOI: https://doi.org/10.1007/s00233-014-9571-6

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