Polynomials

Related lectures (31)

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Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Explores the uniqueness of minimal polynomials and the division algorithm for polynomials.

Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.

Explores division polynomials, theorems, spectral values, and minimal polynomials in endomorphisms and vector spaces.

Covers polynomial factorization examples and polynomial division in complex numbers.

Covers the recap of Galois theory and emphasizes the transitivity of Galois groups.

Covers the Fundamental Theorem of Algebra, polynomial division, and complete factorization of complex polynomials.

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

Covers the Galois correspondence, relating subgroups to intermediate fields.