# If the degree of field extension is a prime number, the extension is simple [closed]

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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## closed as too localized by Akhil MathewApr 4 '11 at 3:09

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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. – Arturo Magidin Apr 4 '11 at 0:08
@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? – Arturo Magidin Apr 4 '11 at 0:34
@user8465: Your Spanish seems pretty good; your attitude, alas, doesn't. – Arturo Magidin Apr 4 '11 at 2:10
@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? – Pete L. Clark Apr 4 '11 at 3:07
@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. – Arturo Magidin Apr 4 '11 at 3:20

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