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Unitally Nondistributive Quantales by García, Javier Gutiérrez; Höhle, Ulrich is a scholarly article available to read on EtoBox.

What is Unitally Nondistributive Quantales about?

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.

Author

García, Javier Gutiérrez; Höhle, Ulrich

Published

2024

Language

EN