Lectures related to Fermat's Equation: Integral Solutions and Gaussian Integers

Explores the Class Number Formula in number theory, focusing on Lemmas, Proofs, and a significant theorem.

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

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

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

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

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

Covers the classification theorem for finite abelian groups and introduces rings, including zero divisors and domains.

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

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

Explores Fermat's Theorem, factorization of integers, properties of Z[i], and Hurwitz quaternions.

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.

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

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

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

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

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

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

Introduces the definition and examples of A-modules, including sub-modules and ideals.