Prüfer and valuation rings with zero divisors

Monte Boisen and Max Dean Larsen

Vol. 40 (1972), No. 1, 7–12

DOI: 10.2140/pjm.1972.40.7

Abstract

Manis has developed a valuation theory on commutative rings with unity producing valuation rings which are not integral domains. Griffin has used the valuation theory of Manis to extend the notion of Prüfer domains to rings with zero divisors, obtaining what Griffin calls Prüfer rings. In this paper, properties of overrings of Prüfer and valuation rings are discussed. An example is given to show that valuation rings need not be Prüfer rings. It is shown that every overring of a Prüfer valuation ring is a valuation ring.

Mathematical Subject Classification 2000

Primary: 13F05

Milestones

Received: 8 August 1970

Published: 1 January 1972