Give an example of an algebraic extension of $\mathbb Q$ of degree 3 which is not a normal extension.
Algebraic extension of $\mathbb Q$ but not a normal extension
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galois-theory
2 Answers
1
Hint: Consider the splitting field of the polynomial $x^3-3x+1$ over $\mathbb Q$
1
Hint: if an irreducible degree $3$ polynomial in $\mathbb{Q}[x]$ has complex roots and $a$ is the real root, then $\mathbb{Q}(a)$ is not normal.