Generating ideals in Prüfer domains

Raymond Heitmann

Vol. 62 (1976), No. 1, 117–126

DOI: 10.2140/pjm.1976.62.117

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