nLab
fractional ideal

Given a commutative domain kk, a fractional ideal of kk in the quotient field Q(k)Q(k) is a kk-submodule MQ(k)M\subset Q(k) such that there exist an element ckc\in k such that cMkc M\subset k.

If kk is Noetherian domain, then cMc M is finitely generated, and hence MM is also a finitely generated kk-module.

Fractional ideals are of importance in algebraic number theory.

Created on July 25, 2011 at 22:16:24. See the history of this page for a list of all contributions to it.