3
$\begingroup$

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 $f : k[x_1,\ldots,x_n]\rightarrow k(y_1,\ldots, y_m)$

  • 5
    This looks like homework. What have you tried?2011-04-25
  • 2
    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.2011-04-25
  • 0
    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)$2011-04-25
  • 0
    @Sam: How about adding that to the question and rephrasing it so it doesn't sound like you're the teacher, we're the students, and you are giving us homework? Then, if you are stuck somewhere, you can say exactly where and ask for help specific to whatever is blocking your way.2011-04-25
  • 1
    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.2011-04-25
  • 1
    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.2011-04-25
  • 0
    @Sam: "Imperative mode" is the tense in which the original problem is written; it is the standard tense to write problems and theorems, but it is a rather bad tense to ask questions: it is used to issue **orders**, which you are not doing. So, yes, problems in book are almost invariably written in imperative mode. This is not something we "consider" or "don't consider", it's a simple matter of grammar.2011-04-26
  • 0
    @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

0 Answers 0