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.
The structure of finite commutative idempotent involutive residuated lattices / P. Jipsen, O. Tuyt, D. Valota. - In: ALGEBRA UNIVERSALIS. - ISSN 0002-5240. - 82:4(2021 Sep 16), pp. 57.1-57.23. [10.1007/s00012-021-00751-4]
The structure of finite commutative idempotent involutive residuated lattices
D. ValotaUltimo
2021
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.File | Dimensione | Formato | |
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