Some properties of complete congruence lattices
By: R. Giacobazzi and F. Ranzato
Roberto
Giacobazzi
Dip. di Informatica
Univ. di Pisa
Corso
Italia 40, 56125 Pisa
(Italy)
giaco@di.unipi.it
Abstract:
For a complete lattice C, we consider the
problem of determining 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.
Mathematics Subject Classification
06B10 (06A15, 06A23
06D15).
Available: DVI,
PostScript,
BibTeX Entry.
This result is a consequence of our research in abstract
interpretation completeness:
giaco@sci.univr.it