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.
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Received January 6, 1998; accepted in final form July 2, 1998.
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Giacobazzi, R., Ranzato, F. Some properties of complete congruence lattices. Algebra univers. 40, 189–200 (1998). https://doi.org/10.1007/s000120050089
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DOI: https://doi.org/10.1007/s000120050089