Algebraic Geometry: Rings and Bodies

Related lectures (32)

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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.