Hi.
There is a really quick proof of the Nullstellensatz when the field is infinite (**edit : I meant uncountable**) (let's take $\mathbb{C}$ for example.) 
It mainly uses the fact that $\mathbb{C}(x)$ is an extension of C of infinite and uncountable dimension. 


I would like to know where (from who ? When ?) this idea came from ? I know that the well-known proof using entire rings and Noether normalisation came from Zariski, but I found nothing concerning this idea. 


Thanks.



Origin of the elementary proof of the Nullstellensatz with an uncountable field
If this is the proof I think it is, in Exercise 4.31 of Eisenbud's book on commutative algebra he attributes it to Krull and van der Waerden.


