The structure of finite commutative idempotent involutive residuated lattices
Logic
2021-08-27 v4
Abstract
We characterize commutative idempotent involutive residuated lattices as disjoint unions of Boolean algebras arranged over a distributive lattice. We use this description to introduce a new construction, called gluing, that allows us to build new members of this variety from other ones. In particular, all finite members can be constructed in this way from Boolean algebras. Finally, we apply our construction to prove that the fusion reduct of any finite member is a distributive semilattice, and to show that this variety is not locally finite.
Keywords
Cite
@article{arxiv.2007.14483,
title = {The structure of finite commutative idempotent involutive residuated lattices},
author = {Peter Jipsen and Olim Tuyt and Diego Valota},
journal= {arXiv preprint arXiv:2007.14483},
year = {2021}
}