Relatively inherently nonfinitely q-based semigroups
Marcel Jackson, Mikhail Vladimirovich Volkov · Transactions of the American Mathematical Society · 2008
We prove that every semigroup S \mathbf {S} whose quasivariety contains a 3-nilpotent semigroup or a semigroup of index more than 2 has no finite basis for its quasi-identities provided that one of the following properties holds: S \mathbf {S} is finite; S \mathbf {S} has a faithful representation by injective partial maps on a set; S \mathbf {S} has a faithful representation by order preserving maps on a chain. As a corollary it is shown that, in an asymptotic sense, almost all finite semigroups and finite monoids admit no finite basis for their quasi-identities.