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Related lectures (31)

Page 2 of 4

Galois Theory: Recap and Transitivity

Covers the recap of Galois theory and emphasizes the transitivity of Galois groups.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Galois Theory: Extensions and Residual Fields

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

Decomposition & Inertia: Group Actions and Galois Theory

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

Galois Theory Fundamentals

Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.

Galois Theory of Qp

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

Ramification Theory: Residual Fields and Discriminant Ideal

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

P-adic Numbers: Completion and Norm

Explores the definition of Q_p and the completion of Q,1(p) to form Qp.

Extension of Fields: Norm and Valuation

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

Algebraic Extensions

Explores algebraic extensions, constructions, irreducible polynomials, autonomous constructions, and cutting compositions.