Galois Theory Fundamentals

Related lectures (32)

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.

Revisits the Galoisian correspondence and explores group actions in intermediate coatings.

Explores Galois fields, elliptic curve cryptography, arithmetic operations, group structure, and practical examples in cryptography.

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.

Introduces Galois fields, elliptic curves, factorization algorithms, and the discrete logarithm problem in cryptography.

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

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

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

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