Join-completions of ordered algebras
Jos\'e Gil-F\'erez, Luca Spada, Constantine Tsinakis, Hongjun Zhou
TL;DR
This paper systematically studies join-extensions and join-completions of ordered algebras, simplifying key results and constructions in ordered structure theory, including Dedekind-MacNeille completions and finite embeddability.
Contribution
It provides a unified, refined framework for join-completions in ordered algebras, enhancing understanding of fundamental properties and constructions.
Findings
Simplified proofs of Dedekind-MacNeille completion properties
Refined treatment of join-extensions in ordered algebras
Established finite embeddability property for various algebraic varieties
Abstract
We present a systematic study of join-extensions and join-completions of 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 ordered algebras.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras · Rough Sets and Fuzzy Logic