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I've come across this problem in Etingof's notes on representation theory (Problem 5.1 on p. 78). It just sounds nice exercise... The question is :

Let $f : k(x_1,\ldots,x_n)\rightarrow k(y_1,\ldots, y_m)$ be a field embedding of field of rational functions. Show that $m\geq n$.

P.S: His hint was first to show for $f : k[x_1,\ldots,x_n]\rightarrow k(y_1,\ldots, y_m)$

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    @Sam: If all you are doing is "sharing a problem" you think is interesting, then *that* is something you should state in your question. It's polite, useful (to potential answerers), and much better to give some context to the question, rather than simply copy it in imperative mode from whichever source you got it from.2011-04-26

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