Suppose that $M$ is a finitely generated module over $A=k[X\_1,\ldots,X\_n]$ of Krull dimension $m$ with $k$ an infinite field. Then one version of Noether normalisation says there is an $m$-dimensional $k$-subspace $W$ of the $k$-vector space spanned by $X\_1,\ldots,X\_n$ such that $M$ is finitely generated over $\operatorname{Sym}(W)$ considered as a subring of $A$. 


As is surely well-known, in fact one can show that the set of $m$-dimensional $k$-vector spaces $W$ that work is open in the appropriate Grassmannian. My question is where is there a reference for this fact in the literature?



Generic Noether normalisation
Ok, I might be missing something (I often am) but I believe that [this](http://books.google.com/books?id=7ua4WsmpDbMC&pg=PA453&lpg=PA453&dq=noether+normalization+works+generically&source=bl&ots=Rb24oAphIe&sig=fXu2RhCrSf77Dyi0IYHg-mmXMMM&hl=en&ei=ODveSo_2KsbV8AbsiJFn&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBgQ6AEwAw#v=onepage&q=&f=false) does it. Scroll up to page 452, line 3.9. The book is Effective Methods in Algebraic Geometry by Rossi and Spangher.


