Corollary 2

Tag 05IM, permanent. Cite it as [Bourbaki, Tag 05IM].

Algebra, chapter I, § 9. Fields

Let $\mathbf{A}$ be a commutative ring which is not 0. There exists a homomorphism of $\mathbf{A}$ onto a commutative field.

By Krull’s Theorem ( $§ 8$ , no. 6, Theorem 1), there exists in $\mathbf{A}$ a maximal ideal $a$ . Then $\mathbf{A}/a$ is a field (Corollary 1).

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

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