Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Covers rings, modules, fields, minimal ideals, and the Nullstellensatz theorem.
