Dualisability of Finite Semigroups

Decidability and Tameness in the Theory of Finite Semigroups

The Complexity of Dualisability: Three-Element Unary Algebras

Perhaps the most fundamental problem in the theory of natural dualities is the dualisability problem: deciding exactly which finite algebras generate a quasivariety that admits a natural duality. One of the goals of this paper is to demonstrate the difficulty of this problem. To do this, we solve the dualisability problem restricted to a class of apparently very simple algebras: three-element u...

Natural Dualities for Semilattice-based Algebras

While every finite lattice-based algebra is dualisable, the same is not true of semilattice-based algebras. We show that a finite semilattice-based algebra is dualisable if all its operations are compatible with the semilattice operation. We also give examples of infinite semilattice-based algebras that are dualisable. In contrast, we present a general condition that guarantees the inherent non...

Classification of Monogenic Ternary Semigroups

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

and Beyond

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