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Related lectures (15)
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Dedekind Rings: Factorisation and Ideal Class Group
Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.
The Discriminant and Ideal Class Group in Mathematics
Explores the discriminant in matrices, ideal class groups, and optimal embeddings in mathematics.
Ideal Class Group Relations
Covers the relations between the ideal class group and proper fractional ideals.
Hermite-Minkowski Theorems: Number Fields and Ideal Classes
Explores Hermite-Minkowski theorems in number fields and ideal classes.
Number Fields: Embeddings and Ideal Classes
Covers the embeddings of number fields and ideal classes with proofs and examples.
Logarithmic Embedding in Number Fields
Explores the properties and applications of logarithmic embeddings in number fields.
Dedekind Rings and Fractional Ideals
Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.
Embeddings of Number Fields
Explores embeddings of number fields, types, signatures, lattices, and determinants.
Dedekind Rings: Theory and Applications
Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.
Integral Representations: Quadratic Lattices and Hasse Principle
Explores integral representations, quadratic lattices, and the Hasse Principle.
Galois Theory: Dedekind Rings
Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.
Frobenius Theorems in Number Theory
Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.
Ramification Theory: Dedekind Recipe
Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.
Localization and Ideals
Covers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.
Ramification Theory: Residual Fields and Discriminant Ideal
Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.
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