Original Articles

RADICAL PARTITIONING

Published in: Quaestiones Mathematicae
Volume 5, issue 4, 1983, pages: 331–339
DOI: 10.1080/16073606.1983.9632275
Author(s): H.J. le Roux, Republic of South Africa, T.L. Jenkins, U.S.A.
Keywords: 16A12, 16A21, 16A22

Abstract

A radical class R partitions a class of rings T if for every T ε T either R(T) = 0 or R(T) = T. Given any class of rings C, Stewart [8] defines the class of almost C-rings, A(C), to be all those rings every non identity homomorphic image of which is in C. He then defines C to be the class of all rings S where S is the heart of a ring A with A/S in C. He then considers the general question: what radical classes partition the class of almost C-rings where C has certain properties. With the aid of M*-rings introduced in this paper we can generalize some of Stewart's results and obtain more natural partitions.

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