Unitally nondistributive quantales

  • Javier Gutiérrez García

    Universidad del País Vasco (UPV/EHU), Bilbao, Spain
  • Ulrich Höhle

    Bergische Universität, Wuppertal, Germany
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Abstract

Unitally nondistributive quantales are unital quantales such that the unit is approximable by the totally below relation and does not meet-distribute over arbitrary joins. It is shown that the underlying nondistributive complete lattice contains at least elements. Moreover, under mild conditions, every quantale has an extension to a unitally nondistributive quantale by the addition of an isolated unit. As a byproduct of this construction we prove that there exist non-isomorphic, unitally nondistributive quantales on the set of elements.

Cite this article

Javier Gutiérrez García, Ulrich Höhle, Unitally nondistributive quantales. Port. Math. 82 (2025), no. 3/4, pp. 259–280

DOI 10.4171/PM/2140