Lectures related to Algebraic extension

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

Explores transcendence degree in algebraic fields and classical analytic functions.

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

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

Explores purely inseparable decompositions, Galois property, and algebraic closures.

Covers the algebraic closure of Qp and the definition of p-adic complex numbers, exploring roots' continuous dependence on coefficients.

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

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

Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.

Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

Covers the Jordan Normal Form and the identification of torsion blocks within matrices.

Explores homomorphisms in topology and delves into Galois theory.

Explores the algebraic properties of the cross product and its linearity.

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

Covers error-correcting codes, Hamming distance, and polynomial multiplication in algebraic fields.

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

Covers the completion of a field, focusing on algebraic closure and function convergence.

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

Covers the Gauss-Wantzel Theorem and Fermat prime numbers.