English

Unitally nondistributive quantales

General Topology 2024-12-02 v3

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 77 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 3030 non-isomorphic, unitally nondistributive quantales on the set of 77 elements.

Keywords

Cite

@article{arxiv.2402.17284,
  title  = {Unitally nondistributive quantales},
  author = {Javier Gutiérrez García and Ulrich Höhle},
  journal= {arXiv preprint arXiv:2402.17284},
  year   = {2024}
}

Comments

16 pages, 8 figures

R2 v1 2026-06-28T15:01:33.718Z