Lectures related to Algebraic Geometry: Rings and Bodies

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

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

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

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.

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

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

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

Explores irreducible polynomials, finite fields, and the construction of unique finite fields from irreducible polynomials.

Explores the uniqueness of minimal polynomials and the division algorithm for polynomials.

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

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

Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.

Explores the Chinese remainder theorem, systems of congruences, and Euclidean domains in integer numbers and polynomial rings.

Covers the factorization of polynomials over a field, including division with remainder and common divisors.