One-dimensional domain

Definition
An integral domain is termed a one-dimensional domain if it satisfies the following equivalent conditions:


 * Every nonzero prime ideal in it is maximal
 * It has Krull dimension at most one (note that the Krull dimension is zero iff it is a field)

Stronger properties

 * Weaker than::Field
 * Weaker than::Polynomial ring over a field
 * Weaker than::Ring of integers in a number field
 * Weaker than::Principal ideal domain
 * Weaker than::Dedekind domain

Weaker properties

 * Stronger than::Finite-dimensional domain
 * Stronger than::Finite-dimensional ring