Join-completions of partially ordered algebras

We present a systematic study of join-extensions and join-completions of partially ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and constructions in the theory of ordered structures ranging from properties of the Dedekind–MacNeille completion t...

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Bibliographic Details
Published in:Annals of pure and applied logic 2020-12, Vol.171 (10), p.102842, Article 102842
Main Authors: Gil-Férez, José, Spada, Luca, Tsinakis, Constantine, Zhou, Hongjun
Format: Article
Language:English
Subjects:
Finite embeddability property
Join-completion
Lattice-ordered group
Nucleus
Partially ordered algebra
Residuated lattice
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Summary:We present a systematic study of join-extensions and join-completions of partially ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and constructions in the theory of ordered structures ranging from properties of the Dedekind–MacNeille completion to the proof of the finite embeddability property for a number of varieties of lattice-ordered algebras.
ISSN:0168-0072
DOI:10.1016/j.apal.2020.102842