Regular congruence-preserving extensions of lattices. (Q1771864)

The authors prove that every lattice \(L\) has a congruence-preserving extension to a regular lattice \(\bar L\) where every compact congruence of \(\bar L\) is principal. The construction of \(\bar L\) is done by iterating a construction of the first author and F. Wehrung and taking direct products. They also discuss the case of a finite lattice \(L\) for which \(\bar L\) can be chosen to be finite, and of a lattice \(L\) with zero, in which case \(\bar L\) can be chosen to have zero and the extension can be chosen to preserve zero.