Vol. 58, No. 2, 1975

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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