# Noetherian domain

From Commalg

This article defines a property of integral domains, viz., a property that, given any integral domain, is either true or false for that.

View other properties of integral domains | 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

## Contents

## Definition

### Symbol-free definition

An integral domain is termed a **Noetherian domain** if every ideal in it is finitely generated. In other words, it is both an integral domain and a Noetherian ring.

## Relation with other properties

### Stronger properties

### Weaker properties

## Metaproperties

### Polynomial-closedness

This property of integral domains is closed under taking polynomials, i.e., whenever an integral domain has this property, so does the polynomial ring in one variable over it.

View other polynomial-closed properties of integral domains OR view polynomial-closed properties of commutative unital rings