Definition 2

Tag 04GG, permanent. Cite it as [Bourbaki, Tag 04GG].

Commutative Algebra, chapter III, § 3. m-adic topologies on Noetherian rings

A topological ring $A$ is called a Zariski ring if it is commutative and Noetherian and there exists a defining ideal $m$ for the topology on $A$ satisfying the equivalent conditions of Proposition 6.

A Zariski ring $A$ is necessarily Hausdorff (Proposition 6) and every defining ideal of its topology is contained in the Jacobson radical of $A$ .

Examples of Zariski rings

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Proposition 6