Abstract
As defined by Arens and Kaplansky [2] a ring A is strongly regular (s.r.) in case to each a∊ A there corresponds x = xa
∊A depending on a such that a
2
x = a. In the present article a ring A is defined to be a s.r. extension of a subring B in case each a>∊A satisfies a
2
x-a∊B with x = xa
∊A. S.r. rings are, then, s.r. extensions of each subring. A ring A which is a s.r. extension of the center has been called a ξ-ring (see Utumi [13], Drazin [3], Martindale [11], and their bibliographies).
Publisher
Cambridge University Press (CUP)