A note on determinability of free objects in four classes of strong doppelsemigroups

Abstract

The problem of determinability of free algebras in a given variety up to an isomorphism by their endomorphism semigroups, originating in B. Plotkin’s universal algebraic geometry, is a classical question in algebra. We prove that the free strong doppelsemigroup, the free commutative strong doppelsemigroup, the free \(n\)-dinilpotent strong doppelsemigroup, and the free \(n\)-nilpotent strong doppelsemigroup are determined up to an isomorphism by their endomorphism semigroups.