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Lecture
Galois Theory: Recap and Transitivity
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Related lectures (34)
Topology: Homomorphisms and Galois Theory
Explores homomorphisms in topology and delves into Galois theory.
Classification of Extensions
Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.
Galois Correspondence
Covers the Galois correspondence, relating subgroups to intermediate fields.
Cohomology: Cross Product
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Intermediate Coatings: Revisiting Galoisian Correspondence
Revisits the Galoisian correspondence and explores group actions in intermediate coatings.
Bar Construction: Homology Groups and Classifying Space
Covers the bar construction method, homology groups, classifying space, and the Hopf formula.
Group Cohomology
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
First Isomorphism Theorem
Covers the first isomorphism theorem in group theory and its applications.
Ramification and Structure of Finite Extensions
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Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.
Galois Theory Fundamentals
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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.
Finite Degree Extensions
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Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.
Galois Theory: The Galois Correspondence
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Explores the Galois correspondence and solvability by radicals in polynomial equations.
Galois Theory: Extensions and Residual Fields
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Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.
Galois Theory of Qp
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Explores the Galois theory of Qp, covering algebraic extensions, inertia groups, and cyclic properties.
Decomposition & Inertia: Group Actions and Galois Theory
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Explores decomposition groups, inertia subgroups, Galois theory, unramified primes, and cyclotomic fields in group actions and field extensions.
Galois Theory: Solvability and Radical Extensions
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Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.
Purely Inseparable Decompositions
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Explores purely inseparable decompositions, Galois property, and algebraic closures.
Hensel's Lemma and Field Theory
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Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.
Dimension Theory of Rings
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Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.
Algebraic Extensions and Decomposition of Fok [x]
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Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].
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