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Finite extension

by luciasiti
Tags: extension, finite
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Jan3-13, 04:48 AM
P: 4
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?
Thanks for your help!
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Jan3-13, 05:16 AM
micromass's Avatar
P: 18,080
What algebraic extensions do you know of [itex]\mathbb{Q}[/itex]??
Jan3-13, 05:17 AM
Sci Advisor
PF Gold
P: 39,353
Let L be the set of rational numbers and K the set of all algebraic numbers.

Jan3-13, 06:26 PM
P: 4
Finite extension

Quote Quote by micromass View Post
What algebraic extensions do you know of [itex]\mathbb{Q}[/itex]??
[itex]\mathbb{Q(\sqrt{2})}[/itex] is an algebraic extension of [itex]\mathbb{Q}[/itex]

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