Remark 4

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

Algebra, VIII, p. 148, § 8. Semisimple Rings

Suppose that the ring A is semisimple. Let $(e_i)_{i\in I}$ be a partition of 1 consisting of nonzero idempotents in the center Z of A. If Card(I) = Card( $\mathscr{S}$ ), then the $e_i$ are the indecomposable idempotents in Z.

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

Proposition 10, § 21

Cites

Nothing.