Integrally closed subring

This article defines a property that can be evaluated for a unital subring in a commutative unital ring: given any commutative unital ring and a subring thereof, the property is either true or false for the pair
View a complete list of such properties

Definition

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 notions

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