(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'll be delighted to get an answer to the following question:

Does every algebraic extension of a field is a simple extension?

2. Relevant equations

3. The attempt at a solution

I'm pretty sure that the answer is negative... I was thinking on taking the field of all the algebraic numbers over [tex] Q [/tex] ... this field is obviously an algebraic extension of Q, but how can I prove it isn't simple? (I'm pretty sure that its degree is infinity, but have no idea how to to prove it) ...

Hope you'll be able to help me

Thanks!

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# Homework Help: Algebraic And Simple Extensions

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