Zero-dimensional ring

Symbol-free definition
A commutative unital ring is termed zero-dimensional if it satisfies the following equivalent conditions:


 * It has Krull dimension zero
 * Every prime ideal in it is maximal
 * Any quotient ring of it that is an integral domain is also a field
 * The spectrum of the ring is a T1 space i.e. all points in the spectrum are closed

Conjunction with other properties

 * Zero-dimensional Noetherian ring: A zero-dimensional ring that is also a Noetherian ring.

Stronger properties

 * Weaker than::Finite ring
 * Weaker than::Field
 * Weaker than::Finite-dimensional algebra over a field
 * Weaker than::Artinian ring
 * Weaker than::Semisimple ring

Weaker properties

 * Stronger than::Jacobson ring:
 * Cohen-Macaulay ring (under the assumption that the ring is Noetherian):
 * Stronger than::Equidimensional ring