Vol. 40, No. 1, 1972

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 332: 1
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Prüfer and valuation rings with zero divisors

Monte Boisen and Max Dean Larsen

Vol. 40 (1972), No. 1, 7–12
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
Authors
Monte Boisen
Max Dean Larsen