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)


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:
  • Completeness in abstract interpretation: A domain perspective. (AMAST'97 LNCS 1349, 1997).