# Noetherian domain

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

### 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.

## 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.
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