Local Rings and Residues

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Related lectures (31)

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Dimension Theory of Rings

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Ideal Class Group Relations

Covers the relations between the ideal class group and proper fractional ideals.

Algebraic Geometry: Localization and Prime Ideals

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Tangent Spaces in Algebraic Geometry

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Ring Operations: Ideals and Classes

Covers the operations in rings, ideals, classes, and quotient rings.

Dedekind Rings: Theory and Applications

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Idempotent Elements and Central Orthogonal

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.