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5.6 Artin's theorem.

Course video 30 of 55

We apply the discussion from the last lecture to the case of field extensions. We show that the separable extensions remain reduced after a base change: the inseparability is responsible for eventual nilpotents. As our next subject, we introduce normal and Galois extensions and prove Artin's theorem on invariants. This week, the first graded assignment is given.

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