Galois Theory: Recap and Transitivity

Related lectures (34)

Covers the uniqueness of norm extension in finite fields and the construction of norms on finite extensions of Qp.

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

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

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

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

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

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.

Covers Euler's totient function, group theory, homomorphisms, and group isomorphisms.

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

Covers homomorphisms, projective modules, and resolutions in chain complexes.

Covers the approximation of functions in Sobolev spaces using smooth functions.

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