Fractional Ideal - Divisorial Ideal

Divisorial Ideal

Let denote the intersection of all principal fractional ideals containing a nonzero fractional ideal I. Equivalently,

where

(ideal quotient)

If then I is called divisorial. In other words, a divisorial ideal is a nonzero intersection of some nonempty set of fractional principal ideals. If I is divisorial and J is a nonzero fractional ideal, then I : J is divisorial.

An integral domain that satisfies the ascending chain conditions on divisorial ideals is called a Mori domain.