Every nearly idempotent plain algebra generates a minimal variety (Q1902537)

An algebra \(A\) is plain if it is finite, simple and has no non-trivial proper subalgebras. A. Szendrei proved that every idempotent plain algebra generates a minimal variety. This result is here generalized for the so-called nearly idempotent algebras: An algebra \(A\) is nearly idempotent if \(A\) has at least one idempotent and \(\Aut (A)\) acts transitively on the non-idempotent elements. Main result: If \(A\) is nearly idempotent and plain and \(B\in {\mathcal V} (A)\) is plain, then \(A\cong B\). Hence, every nearly idempotent plain algebra generates a minimal variety.