Lectures related to Algebraic Subsets of A^1

Explores ideals with finite sets of points and Hilberts Nullstellensatz in algebraic fields.

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Covers the operations in rings, ideals, classes, and quotient rings.

Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.

Covers the concept of ideals in polynomial rings and their properties.

Covers primary decomposition in commutative rings and its application in prime ideals.

Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

Covers radical ideals, Nullstellensatz, primary ideals, and algebraic sets.

Discusses regular implicit functions, rings, ideals, sheaves, and ring operations.