# Going-down subring

From Commalg

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

### 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 .

## Facts

If is a normal domain and is an integral extension of , then is a going-down subring.