Suppose that $Q⊂L$ is a field extension with $ [L : Q] = 32$. We have to show that 2 is not a third power in $L$.
My try:Actually I could not understand what is required to show .Please help in understanding this one.Thank you.
$Q⊂L$ is a field extension with $ [L : Q] = 32$. Show that 2 is not a third power in $L$.
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field-theory
extension-field
1 Answers
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If $\alpha\in L$ such that $\alpha^3=2$, then $[Q(\alpha):Q]=3$.What can you say about [L:Q] now?
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0I think $9$,correct me if I am wrong. – 2017-02-25
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0@MatheMagic use the tower of fields formula .This will result in $[L:Q]=[L:Q(\alpha)][Q(\alpha):Q]$, so 3 will divide 32, which is impossible.I don't know how you made it to be 9, though. – 2017-02-25
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0sorry.Now i got it.Thank you. – 2017-02-25