Lecture
This lecture introduces affine algebraic sets, starting with the definition of affine space and algebraic sets over a field. It covers the concept of hypersurfaces, affine planes, and elliptic curves, illustrating examples and properties of algebraic subsets. The lecture also discusses the relationship between ideals and algebraic sets, emphasizing the importance of the ground field being algebraically closed. Additionally, it explores the notion of Noetherian rings and modules, showcasing the finitely generated ideals and their corollary in algebraic varieties.