Lectures related to Structure theorem for finitely generated modules over a principal ideal domain

Covers the fundamental theorem of finitely generated modules over a PID.

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

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

Introduces Noetherian modules and explores simple modules and composition series.

Covers the properties of finite dimensional algebras and non-semisimple representations.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Covers the classical Lie algebras, focusing on calculations and dimensions.

Explores the theory of lattices, their properties, and applications in different mathematical contexts, emphasizing local-global principles.

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

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

Explores subrepresentations of the regular representation in group theory, emphasizing properties and isomorphism between subrepresentations.

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

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

Explores flat groups of automorphisms and their properties, including minimization functions and invariance under specific conditions.

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

Explores the Chinese Remainder Theorem for Euclidean domains and the properties of commutative rings and fields.

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.