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.
Read more about this topic: Fractional Ideal
Famous quotes containing the word ideal:
“You’ll never succeed in idealizing hard work. Before you can dig mother earth you’ve got to take off your ideal jacket. The harder a man works, at brute labour, the thinner becomes his idealism, the darker his mind.”
—D.H. (David Herbert)