Given a field $k$ and a finitely generated $k$-algebra $R$ without zero divisors, one knows that there exist $x\_1, \ldots, x\_n$ algebraically independent such that $R$ is integral over $k[x\_1, \ldots, x\_n]$. 


Does one have a similar statement, under good assumptions, if $k$ is not a field but a ring ? In this discussion, I am also interested by geometric explanations.



Noether's normalization lemma over a ring A
<http://www.math.lsa.umich.edu/~hochster/615W10/supNoeth.pdf>


Supplementary notes from Mel Hochster's commutative algebra class. They discuss, in particular, a generalization of Noether normalization to integral domains.


