P-adic Numbers: Completion and Norm

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Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

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

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

Explores homomorphisms in topology and delves into Galois theory.

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

Covers the Galois correspondence, relating subgroups to intermediate fields.

Introduces algebras over a field, k-linear endomorphisms, and commutative algebras.

Covers matrix calculations, basis change, field extensions, complex numbers modulus, and polar decomposition.

Covers the extension of fields, defining the norm of an element from one field to another, and introducing the p-adic valuation.

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