Abstract
Now that we have developed the machinery of Galois theory, we apply it in this chapter to study special classes of field extensions. Sections 9 and 11 are good examples of how we can use group theoretic information to obtain results in field theory. Section 10 has a somewhat different flavor than the other sections. In it, we look into the classical proof of the Hilbert Theorem 90, a result originally used to help describe cyclic extensions, and from that proof we are led to the study of cohomology, a key tool in algebraic topology, algebraic geometry, and the theory of division rings.
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