Equational theories of unstable involution semigroups

The equational theories of representable residuated semigroups

We show that the equational theory of representable lower semilattice-ordered residuated semigroups is finitely based. We survey related results.

Equational Theories of Semigroups with Enriched Signature

We present sufficient conditions for a unary semigroup variety to have no finite basis for its equational theory. In particular, we exhibit a 6-element involutory semigroup which is inherently non-finitely based as a unary semigroup. As applications we get several naturally arising unary semigroups without finite identity bases, for example: the semigroup of all complex 2 × 2-matrices endowed w...

Definability in the lattice of equational theories of semigroups

We study first-order definability in the lattice L of equational theories of semigroups. A large collection of individual theories and some interesting sets of theories are definable in L . As examples, if T is either the equational theory of a finite semigroup or a finitely axiomatizable locally finite theory, then the set {T, T } is definable, where T ∂ is the dual theory obtained by invertin...

Definability in the Lattice of Equational Theories of Commutative Semigroups

In this paper we study first-order definability in the lattice of equational theories of commutative semigroups. In a series of papers, J. Ježek, solving problems posed by A. Tarski and R. McKenzie, has proved, in particular, that each equational theory is first-order definable in the lattice of equational theories of a given type, up to automorphism, and that such lattices have no automorphism...

Equational Logic and Equational Theories of Algebras