Introduces affine varieties and covers morphisms between them and their coordinate rings.
Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.
Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.
Explains the factorisation of ideals in a Dedekind ring using prime ideals and covers ramification index, residual fields, inertia degree, and properties of Dedekind rings.
