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Article
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MATHEMATICA SCANDINAVICA
Article . 2004 . Peer-reviewed
Data sources: Crossref
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Bounded distributive lattice expansions

Bounded distributive lattice expansions.
Authors: Gehrke, Mai; Jónsson, Bjarni;

Bounded distributive lattice expansions

Abstract

A new notion of a canonical extension $\mathbf{A}^{\sigma }$ is introduced that applies to arbitrary bounded distributive lattice expansions (DLEs) $\mathbf{A} $. The new definition agrees with the earlier ones whenever they apply. In particular, for a bounded distributive lattice $\mathbf{A}, \mathbf{A}^{\sigma }$ has the same meaning as before. A novel feature is the introduction of several topologies on the universe of the canonical extension of a DL. One of these topologies is used to define the canonical extension $f^{\sigma }:\mathbf{A}^{\sigma }\rightarrow \mathbf{B}^{\sigma }$ of an arbitrary map $f:\mathbf{A}\rightarrow \mathbf{B}$ between DLs, and hence to define the canonical extension $\mathbf{A}^{\sigma }$ of an arbitrary DLE $\mathbf{A}$. Together the topologies form a powerful tool for showing that many properties of DLEs are preserved by canonical extensions.

Keywords

Structure and representation theory of distributive lattices, canonical extension algebras, extension of bounded distributive lattices, topologies

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
82
Top 10%
Top 10%
Top 10%
bronze