Remark 1

Tag 0ASQ, permanent. Cite it as [Bourbaki, Tag 0ASQ].

Lie Groups and Lie Algebras, chapter V, § 5. Invariants in the symmetric algebra

It follows from Algebra, Chap. II, §11, no. 4, Prop. 7 that, if $(z_1, \ldots, z_q)$ is a family of homogeneous elements of S whose canonical images in $S/(R_+ S)$ form a basis of $S/(R_+ S)$ over K, then $(z_1, \ldots, z_q)$ is a basis of S over R.

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

Cited by

Theorem 2, § 5

Cites

Algebra, Chap. II, §11, no. 4, Prop. 7