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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.


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Which proof do you mean? The one that I've got in mind is only for an uncountable field. – Charles Siegel May 19 '10 at 15:49
Ow sorry, I meant uncountable field ! – Laurent May 19 '10 at 15:58
up vote 6 down vote accepted

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.

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I looked in Eisenbud's book and yes, thank you that's exactly what I was looking for ! – Laurent May 19 '10 at 16:01

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