Work

Unitally nondistributive quantales

Year: 2025

Type: article

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 7 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 30 non-isomorphic, unitally nondistributive quantales on the set of 7 elements.

Source: Portugaliae Mathematica

DOI: 10.4171/pm/2140

Authors: Javier Gutiérrez García, Ulrich Höhle

Institutions: University of the Basque Country, University of Wuppertal

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Eusko Jaurlaritza

Award: G2748340936