Difference between revisions of "Ring of integers"

Revision as of 17:35, 28 September 2024

Let $K$ be a finite algebraic field extension of $\mathbb{Q}$ . Then the integral closure of ${\mathbb{Z}}$ in $K$ , which we denote by $\mathfrak{o}_K$ , is called the ring of integers of $K$ . Rings of integers are always Dedekind domains with finite class numbers.