Integrally closed subring

Symbol-free definition
A unital subring of a commutative unital ring is said to be integrally closed in the ring if any element of the ring integral over the subring (i.e. satisfying a monic polynomial over the subring) must lie inside the subring itself.

Related ring properties

 * Normal ring is a ring that is integrally closed in its total quotient ring
 * Normal domain is an integral domain that is integrally closed in its field of fractions