# maximal ideals

• November 11th 2008, 08:14 PM
morganfor
maximal ideals
How do you prove that the ideal <x> in Q[x] is maximal?

Thanks!
• November 13th 2008, 07:31 PM
ThePerfectHacker
Quote:

Originally Posted by morganfor
How do you prove that the ideal <x> in Q[x] is maximal?

Thanks!

If $p(x)$ is irreducible then $\left< p(x) \right>$ is maximal.