Polynomials on a Field: Properties and Applications

Related lectures (32)

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

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.

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

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

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

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

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Covers the concept of ideals in polynomial rings and their properties.

Explores operations on ideals and structure theorems in commutative rings.