Zariski ring
In commutative algebra, a Zariski ring is a commutative Noetherian topological ring A whose topology is defined by an ideal contained in the Jacobson radical, the intersection of all maximal ideals. They were introduced by under the name "semi-local ring" which now means something different, and named "Zariski rings" by. Examples of Zariski rings are noetherian local rings with the topology induced by the maximal ideal, and -adic completions of Noetherian rings.
Let A be a Noetherian topological ring with the topology defined by an ideal. Then the following are equivalent.
