Polynomials: Theory and Operations

Related lectures (29)

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

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

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

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

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

Explores ideals in K[X], including PGCD, uniqueness, coprimality, and theorems of Bézout and Gauss.

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

Covers the properties of fields, including irreducibility and units in polynomials.

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

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