Affine Algebraic SetsCovers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Irreducible Algebraic SetsExplores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.
Ideals and PPCMCovers the concept of ideals in polynomial rings and their properties.
Fractions of RingsExplores the concept of fractions of rings and their uniqueness in ideals and quotients.
Local Rings and ResiduesCovers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.
Rings and FieldsExplores rings, fields, ideals, and their properties in algebraic structures.