2024/02/27 by García, Javier Gutiérrez, Höhle, Ulrich
#06B05 #2020: Primary 06F07 Secondary 06A06 #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2402.17284
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.