I am trying to understand this theorem, and as an example I try this case: Let $R=\mathbb{C}[z_1^{\pm},\ldots,z_n^{\pm}]^{S_n}$ be the algebra of Laurent polynomials. Now $R$ should be somehow finitely generated over some polynomial algebra, which I would presume to be $A=\mathbb{C}[s_1,\ldots,s_n]\equiv \mathbb{C}[z_1,\ldots,z_n]^{S_n}$ where $s_i$ are symmetric polynomials. On the other hand, due to the terms $1/z_i$, I think $R$ would be an infinite rank module over $A$.
Probably something is terribly wrong in my reasoning. Which is the polynomial algebra $A$ given by the theorem? Are there any other nice and simple examples of this theorem?
