- #1

mathmari

Gold Member

MHB

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Let $K$ be a normal extension of $F$ and $f\in F[x]$ be irreducible over $F$.

- Let $g_1, g_2$ be irreducible factors of $f$ in the ring $K[x]$. Show that there exists $\sigma \in G(K/F)$ such that $g_2=\sigma (g_1)$.
- If $f$ is reducible over $K$, show that all its irreducible factors in $K[x]$ have the same degree.

I don't really have an idea about that. Could you give me a hint? (Wondering)