Document Type
Article
Publication Date
5-4-2020
Abstract
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.
Recommended Citation
Gil-Férez, J., Jipsen, P. & Metcalfe, G. Structure theorems for idempotent residuated lattices. Algebra Univers. 81, 28 (2020). https://doi.org/10.1007/s00012-020-00659-5
Peer Reviewed
1
Copyright
Springer
Comments
This article was originally published in Algebra Universalis, volume 28, in 2020. https://doi.org/10.1007/s00012-020-00659-5
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