Ring class field

In algebraic number theory, a **ring class field** is an important concept related to algebraic number fields and their class groups. To understand ring class fields, we first need to introduce a few key concepts: 1. **Algebraic Number Field:** An algebraic number field is a finite field extension of the rational numbers \(\mathbb{Q}\). It can be represented as \(\mathbb{Q}(\alpha)\) for some algebraic integer \(\alpha\).