Polynomial Rings and Irreducibility Criteria

Related lectures (30)

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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.