In this post, the lemma used to prove the fundamental theorem of Galois theory is explored, focusing on understanding and proving the lemma itself. The specific lemma discussed relates to field extensions and automorphisms. A concrete example is provided to illustrate the concept, showcasing how different automorphisms transform elements of the fields involved. The proof of the lemma is then presented based on this example, demonstrating how the elements involved relate to each other. This detailed exploration offers valuable insights into the underlying principles of Galois theory without delving into the full theorem itself.
https://susam.net/lemma-for-ftgt.html