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PROFINITE COMPLETIONS AND CANONICAL EXTENSIONS OF SEMILATTICE REDUCTS OF DISTRIBUTIVE LATTICES

Abstract:

A bounded distributive lattice L has two unital semilattice reducts, denoted L̂^ and Lv. These ordered structures have a common canonical extension Lδ. As algebras, they also possess profinite completions, L̂, L̂^ and L̂v; the first of these is well known to coincide with Lδ. Depending on the structure of L, these three completions may coincide or may be di erent. Necessary and sufficient conditions are obtained for the canonical extension of L to coincide with the profinite completion of one...

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Publication status:
Published

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
HOUSTON JOURNAL OF MATHEMATICS
Volume:
39
Issue:
4
Pages:
1117-1136
Publication date:
2013-01-01
ISSN:
0362-1588
Source identifiers:
388045
Language:
English
Keywords:
Pubs id:
pubs:388045
UUID:
uuid:c36e626d-31cb-4005-854b-1d5e0b584c4d
Local pid:
pubs:388045
Deposit date:
2014-02-09

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