The variety of Kleene algebras with conversion is not finitely based
The elements of the full Kleene algebra (with conversion) of a set \(A\) are the binary relations on \(A\), and the operations are those of forming unions, compositions, reflexive, transitive closures and converses of relations. Moreover, the empty relation and the identity relation on \(A\) are included as constants. The variety \(KA^\vee\) generated by all such relation algebras is the variety of Kleene algebras. The variety \(KA\) of conversion-free Kleene algebras is obtained similarly by omitting the conversion operation from the relation algebras. It is known that the equational theory of the variety \(KA\) is not finitely based. In this paper the authors prove in two different ways that the same holds for the variety \(KA^\vee\).
scientific article; zbMATH DE number 1454291