Miroslav Ploscica – Congruence lattices of Abelian l-groups

Safarik's University Kosice, Slovakia

We consider the problem of describing the lattices of compact -ideals of Abelian lattice-ordered groups.
(Equivalently, describing the congruence lattices of Abelian lattice-ordered groups.) It is known that these lattices have
countably based differences and admit a Cevian operation. Our first result says that these two properties are not sufficient:
there are lattices having both countably based differences and Cevian operations, which are not
representable by compact -ideals of Abelian lattice-ordered groups. As our second result, we prove that every
completely normal distributive lattice of cardinality at most admits a Cevian operation.
This complements the recent result of F. Wehrung, who constructed a completely normal distributive lattice
without a Cevian operation of cardinality .