Corollary 2

Tag 04A8, permanent. Cite it as [Bourbaki, Tag 04A8].

Commutative Algebra, chapter II, § 4. Spectra of rings and supports of modules

For the prime spectrum $X = \operatorname{Spec}(A)$ of a ring $A$ to be connected, it is necessary and sufficient that $A$ contain no idempotents other than $0$ and $1$ .

To say that $X$ is not connected means that there exists in $X$ a set which is open and closed and distinct from $\varnothing$ and $X$ .

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

Cited by

Definition 1, § 5

Cites

Nothing.