Remark

Tag 0680, permanent. Cite it as [Bourbaki, Tag 0680].

Algebra, chapter III, § 11. Cogebras, products of multilinear forms, inner products and duality

If M is an A-module such that $M \otimes_A M \neq \{0\}$ , the graded A-algebra (§ 5, no. 1) and graded A-cogebra (no. 1, Example 5) structures on $T(M)$ do not define a bigebra structure, for in general

c(x_1 x_2 y_1 y_2) \neq c(x_1 x_2) c(y_1 y_2)

for four elements $x_1, x_2, y_1, y_2$ of M, as formula (3) of no. 1, shows.

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

Cited by

Nothing.

Cites

§ 5, no. 1