Fractional ideal

In the context of algebraic number theory, a **fractional ideal** is a generalization of the notion of an ideal in a ring. Specifically, fractional ideals are particularly useful in the study of Dedekind domains and more generally in the structure of arithmetic in number fields. ### Definitions and Properties 1. **Integral Domain**: First, consider a domain \( R \), typically a Dedekind domain, which is an integral domain where every nonzero proper prime ideal is maximal.