Definition:Ring of Integers of Number Field

Definition

Let $K$ be a number field.

The ring of integers of $K$, usually denoted $\OO_K$ or $\mathfrak o_K$, is the integral closure of $\Z$ in $K$.

Also see

• Ring of Integers of Number Field is Dedekind Domain

Special cases

• Definition:Ring of Gaussian Integers
• Definition:Ring of Eisenstein Integers

Sources

• 1991: Jürgen Neukirch: Algebraic Number Theory: Chapter $\text I$: Algebraic Integers: $\S 2$ Integrality