Remark

Tag 061E, permanent. Cite it as [Bourbaki, Tag 061E].

Algebra, chapter III, § 4. Tensor products of algebras

Let E be an anticommutative graded A-algebra of type $\mathbf{Z}$ . Then the A-linear mapping of $E \otimes_A E$ into E defined by multiplication of E ( $§ 1$ , no. 3) is a homomorphism of the graded A-algebra $E^g \otimes_A E$ into E, for in the notation of Proposition 14, in the algebra E,

(xy)(x'y') = (-1)^{qp'}(xx')(yy').

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Proposition 14