ON THE STRUCTURE OF EXCHANGE RINGS

An associative ring R with identity is called an exchange ring if R(R) has the exchange property introduced by Crawley and Jonsson [5]. We p rove, in this paper, that if R is an exchange ring with prime factors Artinian, then R is strongly ir-regular. If R is an exchange ring with primitive factors Artinian and R/J(R) is homomorphically semipimitive , then R/J(R) is strongly pi-regular and idempotents lift module J(R). Also, it is shown that for exchange rings, bounded index of nilpotenc e 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.