Remark 1

Tag 009Q, permanent. Cite it as [Bourbaki, Tag 009Q].

Algebra, VIII, p. 145, § 8. Semisimple Rings

Let $\mathfrak{a}$ be a left ideal of A. By the proof above and the corollary of Proposition 12 of II, §1, No. 8, p. 209, the mapping $e\mapsto A(1-e)$ defines a bijection from the set of idempotents $e$ in A such that $\mathfrak{a}= Ae$ to the set of left ideals $\mathfrak{b}$ of A such that $A_s=\mathfrak{a}\oplus \mathfrak{b}$ .

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.

Cites

corollary of Proposition 12 of II, §1, No. 8, p. 209 not in this corpus