The multiplicative fragment of the Yanov equational theory

AbstractWe give a finite equational axiomatization for +-free identities of (regular) languages which contain the empty word. The axioms for the whole equational theory of such languages were given by Yanov

On Equations for Union-Free Regular Languages

AbstractIn this paper we consider the variety UF generated by all algebras of binary relations equipped with the operations of composition, reflexive-transitive closure, and the empty set and the identity relation as constants. This variety coincides with the variety generated by the union-free reducts of Kleene algebras of languages and its free objects are formed by union-free regular languages, that is, regular languages represented by regular expressions having no occurrence of +. We show that the variety UF is not finitely based. The situation does not change if we consider the variety UF∨ generated by the above algebras of binary relations equipped with the conversion operation