On the radical theory of Andrunakievich varieties

Abstract

In 1978 Anderson and Gardner investigated semisimple classes and recently Buys and Gerber developed the theory of special radicals in Andrunakievich varieties. In this note we continue the study of radical theory in Andrunakievich varieties. Sharpening some of the results of Anderson and Gardner we prove versions of Sands' Theorem characterizing semisimple classes by regularity, coinductivity and being closed under extensions. In the proof we follow a new method which avoids calculations with defining identities of the variety. We generalize van Leeuwen's Theorem characterizing semisimple classes of hereditary radicals as classes being regular and closed under essential extensions and subdirect sums.