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Let $L$ be an extension field of $K$. Suppose that the degree $[L:K]$ is a prime number. How to show that $L$ is a simple extension of $K$?

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    Please don't post in the imperative mode; if you have a question on this problem, it's best to say what your question is or where you are stuck and what you have succeeded in doing. Thank you.2011-04-04
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    sorry but my english is not very good,2011-04-04
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    @user8465: It doesn't take much English to pose a question instead of simply issuing an order. What you posted is an order, not a question. I also have to wonder: if you English is so poor that are unable to take this problem and pose it as a question, will you be able to understand the answers you get?2011-04-04
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    @user8465: Your Spanish seems pretty good; your attitude, alas, doesn't.2011-04-04
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    I'm closing this question. @user8465, please some thought in to your questions, instead of simply posing problem after problem.2011-04-04
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    @Akhil: I have no objection to closing the question, but the reason for closing doesn't make much sense to me. I don't think anyone has any trouble seeing what the question is here, and it's not "ambiguous, vague, overly broad or rhetorical". It's true that the OP did not phrase it in the form of a question, but this is not *Jeopardy* -- that's not *really* the reason for closing, is it?2011-04-04
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    @Pete: I don't think the reason for closing (namely, the fact that the OP had asked several poorly motivated questions in succession) is adequately captured by the reasons given. I have, however, changed the reason to "too localized" -- which gives some indication that the OP had not put enough work into it. (That, and it was a question about fields!)2011-04-04
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    @Pete: There was an abusive comment left by the OP (directed at me) which has been deleted. This is no doubt large part of the reason behind the closing and the fact that the OP is suspended for a time.2011-04-04
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    @Pete: What @Arturo said is correct. I would have closed the question regardless of the comment, though the suspension was mostly for it.2011-04-04
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    @Akhil, @Arturo: okay, thanks for the explanation. I well know that the reasons for closure are limited. I just think that "Not a real question" is a rather pointed thing to say, and if someone looks later and sees a "real question" closed for this reason, it looks bad, at least a little bit.2011-04-07

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Hint: If $a\in L$, what are the possible values of $[K(a):K]$?