Example 2

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

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

Every quotient ring $A/b$ of a Zariski ring is a Zariski ring, for it is Noetherian and, if $m$ is a defining ideal of $A$ , $m(A/b) = (m + b)/b$ is contained in the Jacobson radical of $A/b$ (Algebra, Chapter VIII, § 6, no. 3, Proposition 7).

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

Cited by

Nothing.

Cites

*Algebra*, Chapter VIII, § 6, no. 3, Proposition 7