# Ring over which every monic polynomial has finitely many roots

From Commalg

This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring

View all properties of commutative unital ringsVIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions

## Definition

Let be a commutative unital ring. We say that is a **ring over which every monic polynomial has finitely many roots** if every monic polynomial over has finitely many roots, i.e., for any monic polynomial:

,

the set:

is finite.