Lectures related to Center (ring theory)

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

Discusses Fermat's equation and Gaussian integers' properties.

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

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

Covers the properties of the algebra of matrices and related concepts.

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

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

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

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

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

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

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

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

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

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

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

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

Explores modules over a ring, injective morphisms, isomorphisms, and canonical groups.

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

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