1
$\begingroup$

Let $k \subset E$ be a field extension, and let $\alpha$ be algebraic over $k$. Let $f$ be the irreducible polynomial of $\alpha$ over $k$, and let $g$ be the irreducible polynomial of $\alpha$ over $E$. Is it true that $g$ always divides $f$?

$\endgroup$
1
  • $\begingroup$ It is true. It follows directly from the fact, that polynomial rings over fields are PIDs. $\endgroup$ Mar 12, 2017 at 16:33

0

Browse other questions tagged .