In algebraic number theory, the ring of integers of a number field $K$ is the ring of all elements of $K$ which are roots of a monic polynomial with rational integer coefficients.
In algebraic number theory, the ring of integers $\mathcal{O}_K$ of a number field $K$ is the ring of all elements of $K$ which are roots of a monic polynomial with rational integer coefficients. This tag is often used with 'algebraic-number-theory'.
