Radically 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
View a complete list of such properties

Definition

A unital subring $S$ of a commutative unital ring $R$ is termed radically closed if for every $x\in R$ such that there exists $n\ge 1$ for which $x^n\in S$, we have $x\in S$.

Relation with other properties

Stronger properties

• Integrally closed subring
• Algebraically closed subring