Lectures related to Commutative algebra

Primary Decomposition in Commutative Rings

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

Ring Constructions: Structure Theorems

Explores operations on ideals and structure theorems in commutative rings.

Commutativity in Rings

Covers commutativity in rings, evaluation options, and formal linear combinations.

Abélianization: Fundamental Groups

Explores abélianization of fundamental groups in commutative spaces with examples and proofs.

Associative Operations: Fundamentals

Covers associative and commutative operations in parallel programming, using mathematical examples and discussing challenges in preserving associativity.

Modular Arithmetic: Operations and Properties

Explains modular arithmetic operations and properties, including commutative rings and multiplicative inverses.

Modular Arithmetic: Properties and Examples

Covers modular arithmetic properties, computation examples, and commutative rings.

Set Union: Properties and Operations

Explains the union of sets, its properties, operations, and intersection.

Multiplication: Properties and Definitions

Explains the definition and properties of integer multiplication in various scenarios.

Physics 1: Vectors and Dot Product

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Fractional Elements and Equivalence Relations

Explores fractional elements, equivalence relations, and injective mappings in commutative rings.

Natural Numbers

Covers the concept of natural numbers, including properties like commutativity and associativity.

Ideals in Commutative Rings

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Polynomials: Rings and Operations

Covers the basics of polynomials, focusing on rings, operations, and properties.

Intersection: Set Operations

Introduces set intersection, its properties, and its relation to arithmetic operations.

Chinese Remainder Theorem

Explores the Chinese remainder theorem in commutative rings and ideals, demonstrating its applications and relevance in finding unique solutions.

Congruence Relations in Rings

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Rings and Modules: Color Codes and Homological Algebra

Covers rings and modules, emphasizing color codes and homological algebra concepts.

Advanced Linear Algebra

Covers advanced topics in linear algebra, including finite fields, invertible matrices, and vector spaces.