Jipsen, Peter; Tuyt, Olim; Valota, Diego (2021). The structure of finite commutative idempotent involutive residuated lattices. Algebra universalis, 82(4) Springer Nature 10.1007/s00012-021-00751-4
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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.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Tuyt, Olim Frits |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
0002-5240 |
Publisher: |
Springer Nature |
Language: |
English |
Submitter: |
George Metcalfe |
Date Deposited: |
18 May 2022 14:13 |
Last Modified: |
05 Dec 2022 16:19 |
Publisher DOI: |
10.1007/s00012-021-00751-4 |
BORIS DOI: |
10.48350/169832 |
URI: |
https://boris.unibe.ch/id/eprint/169832 |
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