Remark 2
Tag 00FW, permanent. Cite it as [Bourbaki, Tag 00FW].
Algebra, VIII, p. 242, § 13. Absolutely Semisimple Algebras
The assumptions of Theorem 3 are, in particular, satisfied when K is a field and A an absolutely semisimple K-algebra (VIII, p. 238, Theorem 2).
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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Nothing.