# Origin of the elementary proof of the Nullstellensatz with an uncountable field

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.

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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