On the structure of principal ideal rings

Abstract

In this paper all rings are supposed commutative with identity (and all ring direct sums are finite). We distinguish between a principal ideal domain (PID) and a principal ideal ring (PIR) which may not be an integral domain. Our chief purpose is to prove: THEOREM 1. Every principal ideal ring R is a direct sum of rings, each of which is the homomorphic image of a principal ideal domain. © 1968 by Pacific Journal of Mathematics.