n-generator ideals in Prüfer domains

Richard Gordon Swan

Vol. 111 (1984), No. 2, 433–446

DOI: 10.2140/pjm.1984.111.433

Abstract

Heitmann has shown that a finitely generated ideal in a Prüfer domain of Krull dimension n needs at most n + 1 generators. I will show here that this result is, in fact, the best possible. The same is true for Heitmann’s stability theorems.

Mathematical Subject Classification 2000

Primary: 13F05

Secondary: 13A15, 13G05

Milestones

Received: 12 April 1982

Published: 1 April 1984