# Field Extension

• Dec 30th 2008, 11:26 AM
peteryellow
Field Extension
How can I show that there is no finite field extension of \$\mathbb C.\$
• Dec 30th 2008, 11:32 AM
peteryellow
I thought to prove it by contradiction. but then I am having problem to prove it.
• Dec 30th 2008, 01:52 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.