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Lemma for the Fundamental Theorem of Galois Theory
Introduction This post illustrates a key lemma that is used in proving the fundamental theorem of Galois theory (FTGT). Note that FTGT is not covered in this post.
This post illustrates a key lemma that is used in proving the fundamental theorem of Galois theory(FTGT). Note that Stewart writes \( \tau(M)^{*} = \tau M^* \tau^{-1} \) while stating the lemma but I have reversed the LHS and RHS to maintain consistency with the equations that appear in the discussion below. However, in a general proof, \( \tau \) is going to be an arbitrary \( K \)-automorphism of \( L, \) so we cannot know exactly how it behaves and as a result, we cannot obtain the above equation directly.
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