Congruence lattices for varieties of lattices
by
Miroslav Ploščica
Mathematical Institute, Slovak Acad. of Sciences, 04001 Kosice, Slovakia

The general problem is as follows: Which algebraic lattices occur as congruence lattices of algebras from a given variety K? We are mainly interested in the case when K is some variety of lattices. There are very few relevant classes of algebras for which the answer is completely known. Among lattice varieties, the only such class is the variety of distributive lattices. My aim is to present some results for other small lattice varieties. Most of the results are obtained using a topological representation, in which congruences correspond to open subsets of suitable topological spaces.

Date received: July 23, 1999