finite extension


by luciasiti
Tags: extension, finite
luciasiti
luciasiti is offline
#1
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
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#2
Jan3-13, 05:16 AM
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What algebraic extensions do you know of [itex]\mathbb{Q}[/itex]??
HallsofIvy
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#3
Jan3-13, 05:17 AM
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Thanks
PF Gold
P: 38,881
Let L be the set of rational numbers and K the set of all algebraic numbers.

luciasiti
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#4
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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