Ring with equal Krull dimension and global dimension

Definition
A ring with equal Krull dimension and global dimension is a commutative unital ring whose Krull dimension and global dimension are equal (i.e. they're both finite and equal, or both are infinite).

For a general ring, either dimension may be bigger than the other. For instance, an Artinian ring that is not semisimple has zero Krull dimension but nonzero global dimension. There are also examples of rings where the global dimension is smaller than the Krull dimension.

Stronger properties

 * Field
 * Semisimple Artinian ring
 * Principal ideal domain
 * Dedekind domain
 * Regular ring