Lectures related to Class Number Formula

Discusses Fermat's equation and Gaussian integers' properties.

Covers non-degenerate integral quadratic lattices and adèles, including their properties and definitions.

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

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

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.

Explores Diffie-Hellman key exchange, ElGamal cryptosystem, and their security applications in cryptography.

Covers the ring of polynomials, focusing on coefficients and multiplication.

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Covers the proof of Lagrange Theorem and explores quaternions, prime numbers, and equations.

Explores the properties of commutative rings and integral domains in algebra.

Covers commutative ring morphisms, subrings, and injective ring morphisms.

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

Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.

Introduces sub-rings and morphisms in ring theory, emphasizing stability by multiplication.

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Discusses irreducible factors in rings and the properties of Noetherian rings.

Explores F-G sheaf morphisms, sheafification, and localization in ring theory.

Covers polynomials, their operations, division theorem, and provides illustrative examples.