Introduction In the theory of groups, the important concepts of Abelian group, solvable group, nilpotent group, the center of a group and centraliz-ers, are all defined from the binary operation [x,â€¦ (More)

The lattice of all complete congruence relations of a complete lattice is itself a complete lattice. In 1988, the second author announced the converse: every complete lattice L can be represented asâ€¦ (More)

This paper studies the complexity of determining if a finite algebra generates a variety that satisfies various Maltsev conditions, such as congruence distributivity or modularity. For idempotentâ€¦ (More)

Freese and J6nsson [8] showed that the congruence lattice of a (universal) algebra in a congruence modular variety is always arguesian. On the other hand J6nsson [16] constructed arguesian latticesâ€¦ (More)

We focus on varieties T of universal algebras whose congruence lattices are all modular. No further conditions are assumed. We prove that if the variety "{ is residually small, then the following lawâ€¦ (More)

We give a general method for constructing lattices L whose equational theories are inherently nonfinitely based. This means that the equational class (that is, the variety) generated by L is locallyâ€¦ (More)

We will address these questions in order, and provide good partial answers, especially for nite lattices which are bounded homomorphic images of a free lattice. Recall that a nite lattice is boundedâ€¦ (More)

A canonical form for elements of a lattice freely generated by a partial lattice is given. This form agrees with Whitmanâ€™s canonical form for free lattices when the partial lattice is an antichain.â€¦ (More)

R. McKenzie, A. Kostinsky and B. J6nsson have proved the remarkable result that the class of finite sublattices of a free lattice and the class of finite projective lattices coincide [6]. I f weâ€¦ (More)

The main result of this paper is that the class of congruence lattices of semilattices satisfies no nontrivial lattice identities. It is also shown that the class of subalgebra lattices ofâ€¦ (More)