Ideal class group

Related lectures (32)

Explores factorisation in Principal Ideal Domains and the properties of prime numbers.

Covers the properties of the ring of Eisenstein integers and its submodule structure.

Explores integral representations, quadratic lattices, and the Hasse Principle.

Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.

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

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

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Covers the Class Number Formula and a counting problem related to the lattice and Lipschitz principle.

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

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

Covers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

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