The Galois correspondence

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The main result in classical Galois theory is the Galois correspondence which we look at in this video. This relates intermediate fields of a finite extension K/F with subgroups of the corresponding Galois group. When K/F is Galois, this relation is an actual bijection which reverses inclusions. This means that by studying the finite Galois group, we can learn a lot about the field extension. We give some applications, including a proof of the primitive element theorem stating that finite separable extensions can be generated by a single (primitive) element.
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I discovered your channel several mounths ago when I was searching some stuff about cohomology of sheaves, but then just saved your playlist and gave up on that. Now that one popped up and reminded me of what was on my mind, also a good chance to know some Galois theory too I guess :D
Anyways, thank you for your lectures.

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