Every idempotent plain algebra generates a minimal variety
An algebra is called plain if it is finite, simple, and has no nontrivial proper subalgebras. It is shown that for every plain idempotent algebra \({\mathcal A}\), either \({\mathcal A}\) generates a congruence distributive variety, or \({\mathcal A}\) is affine, or \({\mathcal A}\) is term equivalent to a 2-element semilattice or left zero semigroup. This implies the claim in the title. The proof is based on the description of idempotent plain algebras established by the author [in Acta Sci. Math. 51, 251-268 (1987)].
scientific article; zbMATH DE number 4002156