Proposition 1

Tag 0627, permanent. Cite it as [Bourbaki, Tag 0627].

Algebra, chapter III, § 6. Symmetric algebras

The algebra S(M) is commutative.

By definition $\phi'(x)\phi'(y) = \phi'(y)\phi'(x)$ for $x, y$ in M and, as the elements $\phi'(x)$ , where x runs through M, generate S(M), the conclusion follows from § 1, no. 7.

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

Cited by

Nothing.

Cites

§ 1, no. 7