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 $K$?
If the degree of field extension is a prime number, the extension is simple
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abstract-algebra
field-theory
extension-field
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0@Akhil, @Arturo: okay, tha$n$ks for the expla$n$atio$n$. 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
1 Answers
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Hint: If $a\in L$, what are the possible values of $[K(a):K]$?