# Finite extension

1. Jan 3, 2013

### luciasiti

Hi everyone
I 'm having difficulty in proving the following theorem
theorem: If L/K ( L is a field extension of K) is a finite extension then it is algebraic. Show, by an example, that the converse of this theorem is not true, in general.
Can you help me to find an example in this case?

2. Jan 3, 2013

### micromass

Staff Emeritus
What algebraic extensions do you know of $\mathbb{Q}$??

3. Jan 3, 2013

### HallsofIvy

Staff Emeritus
Let L be the set of rational numbers and K the set of all algebraic numbers.

4. Jan 3, 2013

### luciasiti

$\mathbb{Q(\sqrt{2})}$ is an algebraic extension of $\mathbb{Q}$