Definition 3
Tag 00RT, permanent. Cite it as [Bourbaki, Tag 00RT].
Algebra, VIII, p. 441, Appendix 1. Algebras without Unit Element
The radical of the -algebra A, denoted by , is the intersection of the regular maximal left ideals of A.
When A is a ring, every left ideal of A is regular, so the definition of the radical coincides with Definition 2 of VIII, p. 154.
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
Nothing.