William A. Lampe

A property of the lattice of equational theories

It had been conjectured that any algebraic lattice having a compact one could be represented as the lattice of equational theories extending some theory. However, we show that each lattice having such a representation satisfies a nontrivial quasidistributivity condition. In particular,M3 has no such representation.

Dualizability and graph algebras

Abstract We characterize the finite graph algebras which are dualizable. Indeed, a finite graph algebra is dualizable if and only if each connected component of the underlying graph is either complete or bipartite complete (or a single point).

On the congruence lattice characterization theorem

A simplified proof is given for the theorem characterizing the congruence lattice of a universal algebra.

Elementary properties of free extensions

AbstractFor any partial groupoid

The strength of the Grätzer-Schmidt theorem

\mathfrak{A}

Full duality among graph algebras and flat graph algebras

, let Fr

Further properties of lattices of equational theories

\mathfrak{A}