finite extension

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?
Thanks for your help!

micromass

What algebraic extensions do you know of [itex]\mathbb{Q}[/itex]??

HallsofIvy

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

luciasiti

Quote by micromass

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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luciasiti	finite extension Tweet 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!

micromass Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus	What algebraic extensions do you know of [itex]\mathbb{Q}[/itex]??

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	Let L be the set of rational numbers and K the set of all algebraic numbers.