Vol. 66, No. 1, 1976

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Factorization-prime ideals in integral domains

Helen Elizabeth. Adams

Vol. 66 (1976), No. 1, 1–8

In this paper we characterize a new set of prime ideals of an integral domain D, called the set of F-primes of D, that we show to have the following properties: (1) D is the intersection of all DP where P is an F-prime of D;(2) all principal prime ideals and all essential prime ideals (those prime ideals for which DP is a valuation domain) are F-primes; (3) if D is a GCD-domain, then the F-primes of D are precisely the essential primes of D; (4) D is a UFD if and only if the set of F-primes is precisely the set of principal prime ideals of D.

Mathematical Subject Classification 2000
Primary: 13G05
Received: 23 February 1976
Revised: 2 June 1976
Published: 1 September 1976
Helen Elizabeth. Adams