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 with symbols
Suppose is a unital subring of a commutative unital ring . We say that is a going-down subring if given prime idaels of and a prime ideal of lying over (viz , there exists a prime lying over (viz and contained in .