Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Introduces affine varieties and covers morphisms between them and their coordinate rings.
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.
Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.
