Unitally nondistributive quantales
Javier Gutiérrez García, H. Ulrich · Portugaliae Mathematica · 2025
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.