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algebra universalis

, Volume 40, Issue 2, pp 189–200 | Cite as

Some properties of complete congruence lattices

  • R. Giacobazzi
  • F. Ranzato

Abstract.

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.

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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Copyright information

© Birkhäuser Verlag Basel, 1998

Authors and Affiliations

  • R. Giacobazzi
    • 1
  • F. Ranzato
    • 2
  1. 1.Dipartimento di Informatica, Università di Pisa, Corso Italia 40, I-56125 Pisa, Italy, e-mail: giaco@di.unipi.itIT
  2. 2.Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, I-35131 Padova, Italy, e-mail: franz@math.unipd.itIT

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