Algebraic extension

Related lectures (32)

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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.