Integrally closed subring

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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
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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