Self-rectangulating varieties of type 5
Keith A. Kearnes, Ågnes Szendrei
Abstract
We show that a locally finite variety which omits abelian types is self-regulating if and only if it has a compatible semilattice term operation. Such varieties must have a 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.
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