Gauss's lemma (polynomials)

Related lectures (31)

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

Discusses the classification of finite extensions of Qp and introduces Krassner's Lemma on root continuity.

Explores residue fields, quadratic forms, discriminants, and Dedekind recipes in algebraic number theory.

Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

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

Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.