Ramification Theory: Dedekind Recipe

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Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Explores the Galois correspondence and solvability by radicals in polynomial equations.

Explores decomposition groups, inertia subgroups, Galois theory, unramified primes, and cyclotomic fields in group actions and field extensions.

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.

Explores the Galois theory of Qp, covering algebraic extensions, inertia groups, and cyclic properties.

Discusses the classification of finite extensions of Qp and introduces Krassner's Lemma on root continuity.

Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.