Every minimal dual discriminator variety is minimal as a quasivariety

Abstract

Let (†) denote the following property of a variety V: Every subquasivariety ofVis a variety. In this paper, we prove that every idempotent dual discriminator variety has property (†). Property (†) need not hold for nonidempotent dual discriminator varieties, but (†) does hold for minimal nonidempotent dual discriminator varieties. Combining the results for the idempotent and nonidempotent cases, we obtain that every minimal dual discriminator variety is minimal as a quasivariety