Polynomials, Division, and Ideals

Related lectures (32)

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

Covers the properties and operations of complex numbers and their applications.

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

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

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

Delves into using polynomials for combinatorial computations and explores operations and identities with binomial coefficients.

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

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

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

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