Every minimal dual discriminator variety is minimal as a quasivariety (Q829767)

The authors prove the following three theorems: Theorem 1.1. If \(V\) is a minimal dual discriminator variety then \(V\) is minimal as a quasivariety. Theorem 2.3. If \(V\) is an idempotent dual discriminator variety then every of its subquasivariety is a subvariety. Theorem 3.3. Let \(V\) be a minimal filtral variety. If every nontrivial member of \(V\) has a simple subalgbera, then \(V\) is a minimal quasivariety.