Can anyone help me with this problem. I try many ways to solve this but still can't find the solution.Thanks
Let $K$ be a subfield of field $F$, and suppose $f$, $g$ are polynomials in $K[x]$. Let $M_k$ be the ideal generated by $f$ and $g$ in $K[x]$ and $M_f$ be the ideal they generate in $F[x]$.Show that $M_k$ and $M_f$ have the same monic generator