Corollary 1

Tag 04A2, permanent. Cite it as [Bourbaki, Tag 04A2].

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

For a ring $A$ to be such that $X = \mathrm{Spec}(A)$ is irreducible, it is necessary and sufficient that the quotient of $A$ by its nilradical $\mathfrak{N}$ be an integral domain.

By Proposition 11 (i), $\mathfrak{J}(X)$ is the radical of the ideal $(0)$ , that is $\mathfrak{N}$ .

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

Cited by

Nothing.

Cites

Proposition 11