Document Type

Article

Publication Date

9-16-2021

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.

Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Algebra Universalis, volume 82, in 2021 following peer review. The final publication may differ and is available at Springer via https://doi.org/10.1007/s00012-021-00751-4.

A free-to-read copy of the final published article is available here.

Peer Reviewed

1

Copyright

Springer

Available for download on Friday, September 16, 2022

Included in

Algebra Commons

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