On complete congruence lattices of join-infinite distributive lattices (Q1866851)

In 1997, G. Grätzer and E. T. Schmidt raised the problem of characterizing the complete congruence lattices of complete lattices satisfying JID and MID. They proved the theorem: Any complete lattice with more than two elements and with meet-irreducible zero cannot be represented as the lattice of complete congruences of a complete lattice satisfying JID and MID. The author generalizes this result: Theorem 1.2. The lattice of complete congruences of every double frame is a zero-dimensional frame (i.e. its elements are joins of complemented elements).