Lectures related to Hilberts Nullstellensatz and Ideals

Covers algebraic subsets of A^1 and ideals with a finite set of points.

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

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Dimension Theory of Rings

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

Dedekind Rings and Fractional Ideals

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

Ring Operations: Ideals and Classes

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

Primary Decomposition in Rings

Explores primary decomposition in rings, focusing on primary ideals and their properties.

Primary Decomposition in Commutative Rings

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

Ideals and PPCM

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