Definition:Ring of Integers of Number Field

Definition
Let $K$ be a number field.

The ring of integers of $K$, usually denoted $\mathcal O_K$ 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