Concept

Noetherian module

Related lectures (23)

Covers primary decomposition in Noetherian ideals and unique primary ideals.

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

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.

Dedekind Rings: Theory and Applications

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

Dedekind Rings: Integral Extensions and Noetherian Rings

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

Module Theory: Chain Conditions

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

Local Rings and Minimal Primes

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

Module Theory: Noetherian Modules

Introduces Noetherian modules and explores simple modules and composition series.

Irreducible Factors and Noetherian Rings

Discusses irreducible factors in rings and the properties of Noetherian rings.

Affine Algebraic Sets

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Regularity and Noetherian Local Rings

Covers the concepts of regularity and Noetherian local rings in algebraic structures.

Cartier Divisors and Invertible Sheaves

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

Symbolic Powers: Interpretation and Applications

Covers the interpretation and applications of symbolic powers in algebraic structures, focusing on Krull's Hauptideal Satz and Noetherian rings.

Integral Domains: Factorisation and Noetherian Rings

Explores factorisation in Principal Ideal Domains and Noetherian rings, emphasizing the integral closure concept and the factorisation of ideals in Dedekind rings.

Irreducible Factors and Noetherian Rings

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

Discrete Valuation Rings

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

Commutative Algebra: Recollections

Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.

Dedekind Rings: Factorisation and Ideal Class Group

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

Algebraic Structures: Modules and Morphisms

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

Module Theory: Definitions and Examples

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