Ideals: Polynomials and Definitions

Related lectures (32)

Page 1 of 4

Explores the properties and applications of polynomials on a field, including formal derivation and uniqueness.

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

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

Explains the Euclidean algorithm for polynomials over a field K, illustrating its application with examples.

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

Explores polynomial roots, factorization, and the Euclidean algorithm in depth.

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

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

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

Covers the calculation of the greatest common divisor using polynomial methods and the Euclidean algorithm.