Self-Rectangulating Varieties of Type 5
Keith A. Kearnes, Ágnes Szendrei · International Journal of Algebra and Computation · 1997
We show that a locally finite variety which omits abelian types is self-rectangulating if and only if it has a compatible semilattice term operation. Such varieties must have type-set {5}. These varieties are residually small and, when they are finitely generated, they have definable principal congruences. We show that idempotent varieties with a compatible semilattice term operation have the congruence extension property.