IDEAL FACTORIZATION IN STRONGLY DISCRETE INDEPENDENT RINGS OF KRULL TYPE, II

초록

A ZPUI domain D is an integral domain with property ( # ) : every nonzero proper ideal I of D can be written as I = J P1 1 <middle dot> <middle dot> <middle dot> P n , where J is an invertible ideal of D and { P 1 , ... , Pn} n } is a nonempty collection of pairwise comaximal prime ideals of D . Among other things, we study two types of natural generalizations of ZPUI domains: (i) the J in the property ( # ) is principal and (ii) the property ( # ) holds for all nonzero principal ideals of D . For example, we show that (1) D satisfies (i) if and only if D is a ZPUI domain whose invertible ideals are principal and (2) D satisfies (ii) if and only if D is an h-local domain in which each maximal ideal is invertible. We also study the w-operation analogs of these two properties.

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