Document Type
Article
Publication Date
9-9-2023
Abstract
We study varieties generated by semi-primal lattice-expansions by means of category theory. We provide a new proof of the Keimel-Werner topological duality for such varieties and, using similar methods, establish its discrete version. We describe multiple adjunctions between the variety of Boolean algebras and the variety generated by a semi-primal lattice-expansion, both on the topological side and explicitly algebraic. In particular, we show that the Boolean skeleton functor has two adjoints, both defined by taking certain Boolean powers, and we identify properties of these adjunctions which fully characterize semi-primality of an algebra. Lastly, we give a new characterization of canonical extensions of algebras in semi-primal varieties in terms of their Boolean skeletons.
Recommended Citation
Kurz, A., Poiger, W., and Teheux, B. New perspectives on semi-primal varieties. Journal of Pure and Applied Algebra 228, 4 (2023), 107525. https://doi.org/10.1016/j.jpaa.2023.107525
Copyright
Elsevier
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Comments
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Pure and Applied Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Pure and Applied Algebra, volume 228, issue 4, in 2023. https://doi.org/10.1016/j.jpaa.2023.107525
The Creative Commons license below applies only to this version of the article.