Corollary 2

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

Algebra, VIII, p. 215, § 12. Tensor Products of Semisimple Modules

We have $\mathfrak{R}_A(M) =\mathfrak{R}(D)M$ . The A-module M is without radical if and only if the ring D is without radical.

This follows from Proposition 8 of VIII, p. 108 and Theorem 2, b).

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 3, § 12
Proposition 4, § 12

Cites

Proposition 8 of VIII, p. 108
Theorem 2