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Dedekind Rings and Fractional Ideals
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Related lectures (37)
Ideals and Representations
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Covers ideals, representations, modules, and maximal ideals in associative algebras.
Dedekind Rings: Integral Extensions and Noetherian Rings
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Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.
Dimension Theory of Rings
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Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.
Separable Extensions: Dedekind Rings
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Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.
Dedekind Rings: Theory and Applications
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Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.
Simple Modules: Schur's Lemma
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Covers simple modules, endomorphisms, and Schur's lemma in module theory.
Galois Theory: Dedekind Rings
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Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.
Algebraic Geometry: Localization and Prime Ideals
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Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.
Rings and Modules
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Covers rings, modules, fields, minimal ideals, and the Nullstellensatz theorem.
Primary Decomposition in Commutative Rings
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Covers primary decomposition in commutative rings and its application in prime ideals.
Affine Algebraic Sets
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Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Commutative Algebra: Recollections
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Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.
Primary Decomposition in Rings
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Explores primary decomposition in rings, focusing on primary ideals and their properties.
Module Theory: Definitions and Examples
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Introduces the definition and examples of A-modules, including sub-modules and ideals.
Localization Theorem in Dedekind Rings
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Explores the Localization Theorem in Dedekind rings, isomorphism induced by injection, and ramification in field theory.
Local Rings and Residues
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Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.
Dedekind Rings: Factorisation and Ideal Class Group
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Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.
Factorisation in Dedekind Ring
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Explains the factorisation of ideals in a Dedekind ring using prime ideals and covers ramification index, residual fields, inertia degree, and properties of Dedekind rings.
Chinese Remainder Theorem: Rings and Fields
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Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.
Hilberts Nullstellensatz and Ideals
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Explores ideals with finite sets of points and Hilberts Nullstellensatz in algebraic fields.
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