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:
“Our ideal ... must be a language as clear as glass—the person looking out of the window knows there is glass there, but he is not concerned with it; what concerns him is what comes through from the other side.”
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