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.

Read more about this topic:  Fractional Ideal

Famous quotes containing the word ideal:

    And he said, “That ought to make you
    An ideal one-girl farm,
    And give you a chance to put some strength
    On your slim-jim arm.”
    Robert Frost (1874–1963)