Finite-dimensional ring

Symbol-free definition
A finite-dimensional ring is a ring whose Krull dimension is finite.

Stronger properties

 * Artinian ring
 * Zero-dimensional ring
 * One-dimensional ring
 * Local Noetherian ring
 * Multivariate polynomial ring over a field

Conjunction with other properties

 * Finite-dimensional Noetherian ring

Polynomial-closedness
In general, a polynomial ring over a finite-dimensional ring need not be finite-dimensional; when the ring is Noetherian, however, the polynomial ring is finite-dimensional, with dimension exactly one more than that of the original ring.