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Invariance of projective modules in \(\mathsf {Sup}\) under self-duality

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Abstract

Starting from enriched order-theoretic properties of modules over a unital quantale in the category \(\mathsf {Sup}\), this paper presents the following theorem. If the underlying quantale is unital and involutive with a designated element, then the duality of right (left) modules preserves projectivity if and only if the underlying quantale has a dualizing element.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad del País Vasco UPV/EHU, 48080, Bilbao, Spain

    Javier Gutiérrez García

  2. Fakultät für Mathematik und Naturwissenschaften, Bergische Universität, 42097, Wuppertal, Germany

    Ulrich Höhle

  3. Wydział Matematyki i Informatyki, Uniwersytet im. Adama Mickiewicza, 61-614, Poznań, Poland

    Tomasz Kubiak

Authors
  1. Javier Gutiérrez García
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  2. Ulrich Höhle
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  3. Tomasz Kubiak
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Correspondence to Javier Gutiérrez García.

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Communicated by Presented at S. Pulmannova.

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The first named author also acknowledges support from the Basque Government (Grant IT974-16)

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Gutiérrez García, J., Höhle, U. & Kubiak, T. Invariance of projective modules in \(\mathsf {Sup}\) under self-duality. Algebra Univers. 82, 9 (2021). https://doi.org/10.1007/s00012-020-00691-5

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  • DOI: https://doi.org/10.1007/s00012-020-00691-5

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