Rings and Modules: Lecture 1Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.
Compact Manifolds ClassificationCovers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.
Additivity of Dimension & HeightExplores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.
Group Algebra: Maschke's TheoremExplores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.