Finite-dimensional Noetherian ring

Definition
A finite-dimensional Noetherian ring is a commutative unital ring that is both finite-dimensional (i.e. its Krull dimension is finite) and Noetherian (i.e. it satisfies the ascending chain condition on all ideals).

Stronger properties

 * Multivariate polynomial ring over a field
 * Finite-dimensional Noetherian domain
 * Dedekind domain
 * Principal ideal domain

Metaproperties
The polynomial ring over a finite-dimensional Noetherian ring has dimension one more than the original ring.