Polynomial Rings and Irreducibility Criteria

Related lectures (30)

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Introduces polynomial factorization over finite fields and efficient computation of greatest common divisors of polynomials.

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

Covers polynomial division and observer/controller approach with step-by-step examples.

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

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

Explores algebraic structures, classes of examples, and properties of cyclic groups.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Covers the factorization of polynomials over a field, including division with remainder and common divisors.

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.

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