Minimal Characteristic Algebras for Leftmost k-Normal Identities

Abstract

A characteristic algebra for a hereditary property of identities is an algebra [Formula: see text] which generates the variety determined by all identities with that property. We use Płonka's construction, and known minimal characteristic algebras for the k-normality and leftmost properties, to construct minimal characteristic algebras of type (2) for leftmost k-normality for 1 ≤ k ≤ 3, and show that Płonka's construction does not always give a minimal algebra.