Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
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 irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.
Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.
Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.
Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.
