Vol. 62, No. 1, 1976

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Generating ideals in Prüfer domains

Raymond Heitmann

Vol. 62 (1976), No. 1, 117–126

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
Received: 20 February 1975
Revised: 25 September 1975
Published: 1 January 1976
Raymond Heitmann
University of Texas, Austin
Austin TX
United States