The structure of finite commutative idempotent involutive residuated lattices
Publisher DOI
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.
Date Issued
2021
Publication Type
Article
Subject(s)
Language(s)
en
Author(s)
Jipsen, Peter | |
Valota, Diego |
Additional Credits
Journal
Algebra universalis
Publisher
Springer Nature
ISSN
0002-5240
Access(Rights)
open.access