Lectures related to Affine Algebraic Sets

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

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

Dedekind Rings: Integral Extensions and Noetherian Rings

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

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

Hilberts Nullstellensatz and Ideals

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

Simple Modules: Schur's Lemma

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Algebraic Subsets of A^1

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

Algebraic Geometry: Localization and Prime Ideals

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

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.

Primary Decomposition in Rings

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

Irreducible Algebraic Sets

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

Modern Algebraic Geometry

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Irreducible Factors and Noetherian Rings

Discusses irreducible factors in rings and the properties of Noetherian rings.

Rings and Modules

Covers rings, modules, fields, minimal ideals, and the Nullstellensatz theorem.

Irreducible Factors and Noetherian Rings

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

Affine Algebraic Varieties: Zariski Topology

Explores affine algebraic varieties, emphasizing the Zariski Topology and regular functions.

Commutative Algebra: Recollections

Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.

Separable Extensions: Dedekind Rings

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.

Algebraic Varieties: Projective Sets and Topology

Explores projective algebraic sets, prime ideals, irreducible sets, cones, and Nullstellensatz theorem.

Module Theory: Definitions and Examples

Introduces the definition and examples of A-modules, including sub-modules and ideals.