Definition 2

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

Algebra, VIII, p. 154, § 9. Radical

The Jacobson radical (or simply radical) of a ring A, denoted by $\mathfrak{R}(A)$ , is the radical of the A-module $A_s$ , that is, the intersection of the maximal left ideals of A.

By abuse of language, we say that the ring A is without radical if we have $\mathfrak{R}(A) = 0$ .

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

Definition 3, Appendix 1

Cites

Nothing.