Galois Theory Fundamentals

Related lectures (32)

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.

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

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

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.

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

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

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

Discusses the classification of finite extensions of Qp and introduces Krassner's Lemma on root continuity.

Explores algebraic decomposition, simple structures, irreducibility, and separability in finite degrees.

Covers the properties of finite dimensional algebras and non-semisimple representations.

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