Ring of integers in a number field

This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
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Definition

Let $K$ be a number field. Then the ring of integers in $K$, denoted $O_K$, is the subring of $K$ comprising all those elements which are integral over $\mathbb{Z}$, in other words, which satisfy monic polynomials with integer coefficients.

The ring of integers in a number field is also termed a maximal order, here an order is a subring of $K$ which is free as a $\mathbb{Z}$-module, and which, over $\mathbb{Q}$, generates $K$.