Prove that the ring $B = CC[x,y,z,w,v] slash (x y z^2 + w v)$ is not an integral extension over $CC[x,y,z,w]$ and then use Noether's normalization lemma to rewrite it as an integral extension of a polynomial ring.


Prove that the ring $B = CC[x,y,z,w,v] slash (x y z^2 + w^3 v)$ is not an integral extension over $CC[x,y,z,w]$ and then use Noether's normalization lemma to rewrite it as an integral extension of a polynomial ring.