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Unformatted text preview: Mx . 9.5. The Galois Correspondence In this section, we establish the fundamental theorem of Galois theory, a correspondence between intermediate elds K M L and subgroups of Aut K .L/ , when L is a Galois eld extension of K . Proposition 9.5.1. Suppose K L is a nitedimensional separable eld extension. Then there is an element 2 L such that L D K./ . Proof. If K is nite, then the nitedimensional eld extension L is also a nite eld. According to Corollary 3.6.26 , the multiplicative group of units of L is cyclic. Then L D K./ , where is a generator of the multiplicative group of units....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08