Radically closed subring

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{curing-subring property}}

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 $n\geq 1$ for which $x^{n}\in S$, we have $x\in S$.

Relation with other properties

Stronger properties

• Integrally closed subring
• Algebraically closed subring