A generalization of the Wedderburn-Artin theorem

Abstract

The structure of rings such that each of its homomorphic images has the property that each cyclic right module over it is essentially embeddable in a direct summand is determined. Such rings are precisely (i) right uniserial rings, (ii) n × n n \times n matrix rings over two-sided uniserial rings with n > 1 n > 1 , or (iii) sums of rings of the types (i) and (ii).