Some properties of complete congruence lattices

被引：0
|
作者：
R. Giacobazzi
F. Ranzato
机构：
[1] Dipartimento di Informatica,
[2] Università di Pisa,undefined
[3] Corso Italia 40,undefined
[4] I-56125 Pisa,undefined
[5] Italy,undefined
[6] e-mail: giaco@di.unipi.it,undefined
[7] Dipartimento di Matematica Pura ed Applicata,undefined
[8] Università di Padova,undefined
[9] Via Belzoni 7,undefined
[10] I-35131 Padova,undefined
[11] Italy,undefined
[12] e-mail: franz@math.unipd.it,undefined
来源：
algebra universalis | 1998年 / 40卷
关键词：
Key words and phrases: Complete lattice, complete congruence, join- and meet-complete congruence, closure operator, pseudocomplement, continuous complete lattice, meet-continuous complete lattice;
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学科分类号：
摘要：
For a complete lattice C, we consider the problem of establishing when the complete lattice of complete congruence relations on C is a complete sublattice of the complete lattices of join- or meet-complete congruence relations on C. We first argue that this problem is not trivial, and then we show that it admits an affirmative answer whenever C is continuous for the join case and, dually, co-continuous for the meet case. As a consequence, we prove that if C is continuous then each principal filter generated by a continuous complete congruence on C is pseudocomplemented.
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页码：189 / 200
页数：11
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