and named "Zariski rings" by . Examples of Zariski rings are noetherian local rings with the topology induced by the maximal ideal, and $\mathfrak a$ -adic completions of Noetherian rings.

Let A be a Noetherian topological ring with the topology defined by an ideal . Then the following are equivalent.
* A is a Zariski ring.
* The completion is faithfully flat over A (in general, it is only flat over A).
* Every