-1
$\begingroup$

Any finite extension of Q is simple extension of Q? Can someone help me?

$\endgroup$
  • $\begingroup$ Do you know how to google for "simple field extension"? $\endgroup$ – Dietrich Burde Nov 19 '19 at 10:31
2
$\begingroup$

The Primitive Element Theorem says:

Every finite separable field extension is simple.

Since $\mathbb Q$ has characteristic zero, every algebraic extension of $\mathbb Q$ is separable.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.