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!