# Field Extension

• December 30th 2008, 12:26 PM
peteryellow
Field Extension
How can I show that there is no finite field extension of \$\mathbb C.\$
• December 30th 2008, 12:32 PM
peteryellow
I thought to prove it by contradiction. but then I am having problem to prove it.
• December 30th 2008, 02:52 PM
ThePerfectHacker
Quote:

Originally Posted by peteryellow
How can I show that there is no finite field extension of \$\mathbb C.\$

Since $\mathbb{C}$ is algebraically closed it has no proper algebraic extension let alone a finite extension.