Vol. 62, No. 1, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Generating ideals in Prüfer domains

Raymond Heitmann

Vol. 62 (1976), No. 1, 117–126
Abstract

There is a recent theorem that finitely generated ideals in a Prüfer domain of Krull dimension one can be generated by two elements. Whether or not this property holds in Prüfer domains without the dimension assumption is still undecided. However, in this paper, a dimension-dependent bound on the number of generators is derived. Precisely, a finitely generated ideal in an n-dimensional Prüfer domain can be generated by n + 1 elements. In fact, the bound actually holds for invertible ideals in any domain.

Mathematical Subject Classification 2000
Primary: 13F05
Milestones
Received: 20 February 1975
Revised: 25 September 1975
Published: 1 January 1976
Authors
Raymond Heitmann
University of Texas, Austin
Austin TX
United States