Introduces affine varieties and covers morphisms between them and their coordinate rings.
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.
Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.
Explores morphisms, regularity, varieties, local rings, and evaluation morphism in algebraic geometry.
Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.
Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.
