Algebraic Extensions

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Related lectures (32)

Algebraic Geometry: Rings and Bodies Log in to Mediaspace to watch this video

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

Polynomial Factorization over a Field: Eigenvalues Log in to Mediaspace to watch this video

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

Decomposition & Inertia: Group Actions and Galois Theory Log in to Mediaspace to watch this video

Explores decomposition groups, inertia subgroups, Galois theory, unramified primes, and cyclotomic fields in group actions and field extensions.

Matrix Calculations: Basis Change and Extensions Log in to Mediaspace to watch this video

Covers matrix calculations, basis change, field extensions, complex numbers modulus, and polar decomposition.

Gaussian Lemma III: Irreducibility and Primitive Polynomials Log in to Mediaspace to watch this video

Explains irreducibility in polynomial equations and the properties of primitive polynomials.

Galois Theory: Extensions and Residual Fields Log in to Mediaspace to watch this video

Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.

Ramified Extensions: Eisenstein Polynomials Log in to Mediaspace to watch this video

Explores ramified extensions and Eisenstein polynomials, showcasing their applications in mathematical contexts.

Approximation in Sobolev Spaces Log in to Mediaspace to watch this video

Covers the approximation of functions in Sobolev spaces using smooth functions.

Ramification Theory: Residual Fields and Discriminant Ideal Log in to Mediaspace to watch this video

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

Finite Fields: Construction and Properties Log in to Mediaspace to watch this video

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

Residue Fields and Quadratic Forms Log in to Mediaspace to watch this video

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

Built-In Self-Test (BIST): Techniques and Implementations Log in to Mediaspace to watch this video

Explores Built-In Self-Test (BIST) techniques in VLSI systems, covering benefits, drawbacks, implementation details, and the use of Linear Feedback Shift Registers (LFSRs) for test pattern generation.

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