Radicals of rings and subrings

Abstract

1. Introduction. In this paper we examine the relationship between radicals of nonassociative rings and their subrings in certain special situations. The main result of Section 2 is based upon the notion of H-relation introduced in [5]. Suppose W is a class of nonassociative rings (perhaps, indeed, all associative) which is closed under homomorphic images and hereditary to subrings. A relation o-on V/is called an H-relation if the following three properties are satisfied: