Vol. 58, No. 2, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Pre-Prüfer rings

Monte Boisen and Philip B. Sheldon

Vol. 58 (1975), No. 2, 331–344

The purpose of this paper is to investigate the class of pre-Prüfer rings. A ring is defined to be in this class in case each of its proper homomorphic images is a Prüfer ring. It is shown for a domain D that if D is a pre-Prüfer ring, then the prime spectrum of D forms a tree and every finitely generated ideal of D containing a bounded element is invertible. If every finitely generated regularizable ideal of a ring R is invertible, then R is a pre-Prüfer ring. Examples are presented to show that the converse of each of the two results stated above is false.

Mathematical Subject Classification 2000
Primary: 13F05
Received: 29 January 1974
Published: 1 June 1975
Monte Boisen
Philip B. Sheldon