Vol. 42, No. 1, 1972

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A characterization of general Z.P.I.-rings. II

Kathleen B. Levitz

Vol. 42 (1972), No. 1, 147–151
Abstract

A commutative ring R is a general Z.P.I.-ring if each ideal of R can be represented as a finite product of prime ideals. If R is not a general Z.P.I.-ring, it is still possible that each principal ideal of R can be represented as a finite product of prime ideals. In this paper, it is shown that if R is a commutative ring in which each ideal generated by two elements can be written as a finite product of prime ideals, then R must be a general Z.P.I.-ring.

Mathematical Subject Classification 2000
Primary: 13A15
Secondary: 13F05
Milestones
Received: 28 September 1971
Revised: 7 March 1972
Published: 1 July 1972
Authors
Kathleen B. Levitz