Vol. 25, No. 3, 1968

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ISSN: 0030-8730
On the structure of principal ideal rings

Thomas William Hungerford

Vol. 25 (1968), No. 3, 543–547
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.

Mathematical Subject Classification
Primary: 13.50
Milestones
Received: 27 July 1967
Published: 1 June 1968
Authors
Thomas William Hungerford