Math dissertation

Field Theory .  Algebraic extensions: degree, minimal polynomials, adjoining a root.  Existence and uniqueness of splitting fields, algebraic closure.  Finite fields: classification, Frobenius automorphism, cyclicity of finite multiplicative subgroup of a field.  Normal extensions, separable closures, perfect fields, primitive element theorem.  Inseparable extensions.  Galois theory: field embeddings and Galois groups, examples, fundamental theorem in finite case, cyclotomic extensions, norms and traces.  Kummer theory, solvability by radicals via solvable groups.  Examples.  Infinite Galois theory: analogy with the fundamental group of a topological space, Krull topology, fundamental theorem.

Math dissertation

math dissertation

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