Definition 1
Tag 0093, permanent. Cite it as [Bourbaki, Tag 0093].
Algebra, VIII, p. 136, § 8. Semisimple Rings
We say that a ring A is semisimple if it has the equivalent properties (i) through (vi) of Theorem 1. An algebra A over a commutative ring is a semisimple algebra if the ring underlying A is semisimple.
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.
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