Lectures related to The Fundamental Theorem of Finitely Generated Modules

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

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

Explains the independence of events and sets in an algebraic context.

Explores isotypic decomposition in finitely generated C-algebras and its implications, including G-stable ideals and linear projections.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.

Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

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