Radical properties defined locally by polynomial identities II

Abstract

AbstractA radical class R of rings (not necessarily associtative) is called an n-radical class if it has the property that a ring is in R if and only if every subring generated by ≤n elements is in R. A transfer theorem is proved, relating n-radical classes in two universal varieties which share the same ≤n-generator rings. Partially through the use of this result, we obtain information about extension closed subvarieties of various universal varieties of power-associative rings.