Finite Degree Extensions

Related lectures (32)

Page 3 of 4

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

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

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

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

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

Covers the decomposition of a finite field and the concept of roots.

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

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

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

Explores the properties and applications of finite fields, including isomorphism and cyclic properties.