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The Nine Lemma and the push forward construction for special Schreier extensions of monoids with operations

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Abstract

We show that the Nine Lemma holds for special Schreier extensions of monoids with operations. This fact is used to obtain a push forward construction for special Schreier extensions with abelian kernel. This construction permits to give a functorial description of the Baer sum of such extensions.

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Acknowledgements

We wish to express our gratitude to Alex Patchkoria for pointing out to us the existence of some old literature, of not easy access, related to the subject of this paper. This work was partially supported by the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2013, by ESTG and CDRSP from the Polytechnical Institute of Leiria – UID/Multi/04044/2013, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020. This work was partially supported by the Programma per Giovani Ricercatori “Rita Levi-Montalcini”, Funded by the Italian government through MIUR.

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Authors and Affiliations

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

    Nelson Martins-Ferreira

  2. Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milan, Italy

    Andrea Montoli

  3. CMUC and Departamento de Matemática, Universidade de Coimbra, 3001–501, Coimbra, Portugal

    Manuela Sobral

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

Correspondence to Andrea Montoli.

Additional information

Communicated by Lázló Márki.

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Martins-Ferreira, N., Montoli, A. & Sobral, M. The Nine Lemma and the push forward construction for special Schreier extensions of monoids with operations. Semigroup Forum 97, 325–352 (2018). https://doi.org/10.1007/s00233-018-9962-1

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  • DOI: https://doi.org/10.1007/s00233-018-9962-1

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