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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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5  
This looks like homework. What have you tried? – Qiaochu Yuan Apr 25 '11 at 17:24
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In addition to Qiaochu's comment, please rephrase your question as a question, and not in an imperative form. We do not work for you. – Asaf Karagila Apr 25 '11 at 17:32
    
I come across this problem in Etingof's note on representation theory. It just sounds nice exercise. His hint was first to show for $k[x_1.\cdots,x_n]\rightarrow k(y_1,\cdots,y_m)$ – Sam Apr 25 '11 at 19:13
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I did not meant to sound like that. I share a problem that I am thinking about to see anyone has any idea. Probably I am missing something about the policy of forum. @ Karagila : I just send the question in the note. Do we consider problems in a book as imperative tense? It is just sharing nice problems and ideas. – Sam Apr 25 '11 at 22:06
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I've slightly edited your question. However, in Etingof's notes, the hint is much more detailed... Do you want to test us? :) @Asaf: this is a ping since Sam's original ping won't have reached you. – t.b. Apr 25 '11 at 23:18

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