ON THE CANONICAL LATTICE EXTENSION OF A DISTRIBUTIVE NEARLATTICE WITH A RESIDUATION OPERATION
作者:
C.J. Van Alten,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1999)
卷期:
Volume 22,
issue 2
页码: 149-164
ISSN:1607-3606
年代: 1999
DOI:10.1080/16073606.1999.9632069
出版商: Taylor & Francis Group
关键词: 03G10;03G25;06D99;06F35;06F99;08C15
数据来源: Taylor
摘要:
AS shown by Macneille, any distributive nearlattice A has a canonical distributive lattice extension A” that contains A as a hereditary subalgebra. Here, we consider distributive nearlattices A equipped with a binary residuation operation—that, essentially, models the implication connective of Intuitionistic Propositional Logic without the exchange and contraction rules. These form both a category and a quasivariety of algebras. We show that the canonical distributive lattice extension of a such a ‘distributive residuation nearlattice’ AMaybe enriched with a residuation operation which extends that of A and which behaves well with respect to morphisms. We also show that the lattices of relative congruences of A and A° are isomorphic, so that second order properties such as subdirect irreducibility and simplicity are preserved by the extension.
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