Lectures related to Primary decomposition

Primary Decomposition: Noetherian Ideal

Covers primary decomposition in Noetherian ideals and unique primary ideals.

Geometric Primary Decomposition

Covers radical ideals, Nullstellensatz, primary ideals, and algebraic sets.

Primary Decomposition in Rings

Explores primary decomposition in rings, focusing on primary ideals and their properties.

Primary Decomposition in Commutative Rings

Covers primary decomposition in commutative rings and its application in prime ideals.

Module Theory: Chain Conditions

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

Module Structure: Submodules and Ring Ideals

Explains submodules, generated modules, and ring ideals in module structure.

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.

Eigenvalues and Eigenvectors

Covers the concept of eigenvalues and eigenvectors in linear algebra, focusing on the properties of endomorphisms.

Primary Decomposition: Understanding Schemes

Explores primary decomposition and schemes in algebraic geometry, emphasizing the importance of working over non-algebraically closed fields and the concept of fibers of morphisms.

Polynomial Factorization and Decomposition

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.

Primary Decomposition: Behaviour and Localisation

Explores primary decomposition, recovering rings from spectra, and studying regular functions on spectra.

The Ring of Eisenstein Integers: Properties and Applications

Covers the properties of the ring of Eisenstein integers and its submodule structure.

Decomposition of Linear Operators

Covers the decomposition of linear operators and properties of eigenspaces.

Orthonormal Sequences and Hilbert Spaces

Explores orthonormal sequences, Bessel's inequality, and unique decompositions in Hilbert spaces.

Jordan decomposition: Lie algebra

Delves into the Jordan decomposition in Lie algebras of linear algebraic groups.

Module Theory: Noetherian Modules

Introduces Noetherian modules and explores simple modules and composition series.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Group Algebra: Maschke's Theorem

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Cyclic Subspace Decomposition

Explores minimal annihilating polynomials and cyclic invariant subspaces, showcasing their practical applications through matrix computations.

Coulomb Gas and Spin Chain: Quantum Group Applications

Explores the relationship between Coulomb gas models and spin chains in quantum groups.