Corollary

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

Algebra, VIII, p. 224, § 12. Tensor Products of Semisimple Modules

Let L be a separable extension of K. We have $\mathfrak{R}(A_{(L)}) =$ $\mathfrak{R}(A)_{(L)}$ if L is algebraic over K or if the ring A is left Artinian.

This is the case $M = A_s$ of Proposition 10.

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

Proposition 10