Artinian module

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Related lectures (12)

Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.

Module Theory: Chain Conditions

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.

Dimension theory of rings

Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.

Module Theory: Noetherian Modules

Introduces Noetherian modules and explores simple modules and composition series.

Primary Decomposition: Noetherian Ideal

Covers primary decomposition in Noetherian ideals and unique primary ideals.

Module Theory: Definitions and Examples

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Algebraic Structures: Modules and Morphisms

Explores modules, sub-modules, and morphisms in algebraic structures.

Tensor Products of Modules

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Cartier Divisors and Invertible Sheaves

Covers Cartier divisors, invertible sheaves, and their properties in algebraic geometry.

Discrete Valuation Rings

Explores discrete valuation rings, their properties, uniqueness of representation, and relationship with principal ideal domains.

Dedekind Rings: Factorisation and Ideal Class Group

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

Local Rings and Minimal Primes

Explores local rings, Noetherian rings, and minimal primes in the context of integral domains.

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