Example 1

Tag 00AC, permanent. Cite it as [Bourbaki, Tag 00AC].

Algebra, VIII, p. 154, § 9. Radical

If A is a local ring, then it has a unique maximal left ideal $\mathfrak{r}$ , consisting of the noninvertible elements of A (VIII, p. 25, Proposition 1); so $\mathfrak{r}$ is the radical of A. In particular, a field is without radical.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Example 3, § 9
Corollary 4, § 9

Cites

VIII, p. 25, Proposition 1