Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
Covers the isotopic decomposition of modules into simple components and their properties.
Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Introduces affine varieties and covers morphisms between them and their coordinate rings.
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
