Normal radicals of endomorphism rings of free and projective modules

Radical theory for algebras with a scheme of operators

“…As we shall see, the converse is false. The term "normal family" is inspired by the term "normal radical" (see, e.g., [7]). As our first example, therefore, we shall consider normal famifies for the variety of Morita contexts, In this case (Example (7)) the universal idempotents of I are (1,1) and (2,2).…”

“…One conceivable way of getting a radical property for a multiset structure is by combining in some way radical properties of the "components" (which are multioperator groups). We consider this in the final section, and are led to the notion of a normal family of radicals, a generalization of normal radicals as defined by Jaegermann [7].…”

Radicals of rings and subrings

“…R-stable identities pass to centrat extensions and in particular the polynomial ring R [2]. For a discussion of these concepts and their uses in the theory of polynomial identities of nonassociative rings, see ROWEN [7].…”