Galois extension

Related lectures (32)

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

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

Covers the Galois correspondence, establishing a bijection between certain classes of groups and coverings.

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.

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

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

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

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

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

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

Covers matrix calculations, basis change, field extensions, complex numbers modulus, and polar decomposition.

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

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