Linearly 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

A unital subring $S$ of a commutative unital ring $R$ is termed linearly closed if for any $x\in S$ such that $ax=b$ for $a,b\in R$, we have $x\in R$.