finite extension

by luciasiti
Tags: extension, finite
luciasiti is offline
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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micromass is offline
Jan3-13, 05:16 AM
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P: 16,565
What algebraic extensions do you know of [itex]\mathbb{Q}[/itex]??
HallsofIvy is offline
Jan3-13, 05:17 AM
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PF Gold
P: 38,881
Let L be the set of rational numbers and K the set of all algebraic numbers.

luciasiti is offline
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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