On the structure of exchange rings

Abstract

An associative ring R with identity is called an exchange ring if RR; has the exchange property introduced by Crawley and Jon- sson [5]. We prove, in this paper, that if R is an exchange ring with prime factors Artinian, then R is strongly π-regular. If R is an exchange ring with primitive factors Artinian and R/J(R) is homomorphically semipimitive, then R/J(R) is strongly π-regular and idempotents lift modulo J(R). Also, it is shown that for exchange rings, bounded index of nilpotence implies primitive factors Artinian. These are generalizations of the corresponding results in [16], [11], [8] and [2]. Examples are given showing that the generalizations are nontrivial.