Finite Degree Extensions

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This lecture covers the concept of finite degree extensions in Galois theory, focusing on separable extensions and elements of decomposition. It explains the importance of bounded degree and equality in these extensions, with examples and essential steps.

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Ontological neighbourhood

Mathematics

Algebra: Polynomials

Related lectures (32)

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In course

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Instructor

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Ontological neighbourhood

Mathematics

Algebra: Polynomials

Related lectures (32)

Galois Theory Fundamentals

Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.

Galois Theory: Extensions and Residual Fields

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

Galois Theory: The Galois Correspondence

Explores the Galois correspondence and solvability by radicals in polynomial equations.

Purely Inseparable Decompositions

Explores purely inseparable decompositions, Galois property, and algebraic closures.

Galois Theory: Recap and Transitivity

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