Cohomology: Cross ProductExplores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Sheaves and ModulesCovers sheaves and modules, including morphisms, sheafification, cocalization, and direct image properties.
Isotypic DecompositionCovers the isotopic decomposition of modules into simple components and their properties.
Adelic Number TheoryExplores adelic number theory, emphasizing lattices, modules, linear combinations, and Z-linear properties.
Group CohomologyCovers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
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.
Module over a RingExplores modules over a ring, injective morphisms, isomorphisms, and canonical groups.
