Structure theorems for idempotent residuated lattices

Gil Férez, José; Jipsen, Peter; Metcalfe, George (2020). Structure theorems for idempotent residuated lattices. Algebra universalis, 81(2) Birkhäuser 10.1007/s00012-020-00659-5

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In this paper we study structural properties of residuated lattices that are idempotent as monoids. We provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras in various subclasses. We also establish the finite embeddability property for certain varieties generated by classes of residuated lattices that are conservative in the sense that monoid multiplication always yields one of its arguments. We then make use of a more symmetric version of Raftery’s characterization theorem for totally ordered commutative idempotent residuated lattices to prove that the variety generated by this class has the amalgamation property. Finally, we address an open problem in the literature by giving an example of a noncommutative variety of idempotent residuated lattices that has the amalgamation property.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Gil Férez, José and Metcalfe, George

Subjects:

500 Science > 510 Mathematics

ISSN:

0002-5240

Publisher:

Birkhäuser

Language:

English

Submitter:

George Metcalfe

Date Deposited:

27 May 2020 12:19

Last Modified:

27 May 2020 12:27

Publisher DOI:

10.1007/s00012-020-00659-5

ArXiv ID:

2004.09553

BORIS DOI:

10.7892/boris.143923

URI:

https://boris.unibe.ch/id/eprint/143923

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