Remark 3

Tag 00FR, permanent. Cite it as [Bourbaki, Tag 00FR].

Algebra, VIII, p. 238, § 13. Absolutely Semisimple Algebras

We know (VIII, p. 234, Corollary 1) that the tensor product of two absolutely semisimple algebras over a commutative field is absolutely semisimple. Consequently, if the algebra A is absolutely semisimple, then so is the algebra $B = A\otimes_KA^o$ .

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

VIII, p. 234, Corollary 1