Lectures related to Polynomial Rings and Irreducibility Criteria

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.

Explores algebraic decomposition, simple structures, irreducibility, and separability in finite degrees.

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

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

Explores irreducible polynomials, finite fields, and the construction of unique finite fields from irreducible polynomials.

Covers GCD, LCM, and the Euclidean algorithm for efficient computation of GCD.

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

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

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

Covers polynomials, their operations, division theorem, and provides illustrative examples.