Concept

Variety (universal algebra)

Related lectures (23)

Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.

Covers monads as data structures with specific laws and examples like List and Option.

Explores algebraic operations on limits of sequences and discusses the uniqueness of limits and properties of convergent and divergent sequences.

Algebraic Structures of Morphism Spaces

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Complex Numbers: Module and Conjugate

Covers the manipulation of algebraic laws on complex numbers.

Ring Homomorphisms and Ideals

Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.

Algebraic Structures: Classes and Cyclic Groups

Explores algebraic structures, classes of examples, and properties of cyclic groups.

Affine Algebraic Sets

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

Direct Sum of Abelian Groups

Explores the direct sum of abelian groups, emphasizing bijections and uniqueness.

Polynomials and Endomorphisms

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

The Regular Representation

Introduces the regular representation, a key tool for studying group actions on varieties.

Vector Spaces: Properties and Examples

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

Algebraic Geometry: Localization and Prime Ideals

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

Polynomials: Definition and Operations

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Rings and Ideals

Explores rings, domains, fields, and ideals, with a focus on constructions and properties.

Mathematics: Sets and Functions

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Algebraic Structures: Modules and Morphisms

Explores modules, sub-modules, and morphisms in algebraic structures.

Algebraic Structures: Fields and Vectorial Spaces

Covers prime numbers, vectors, 3D geometry, crystallography, and algebraic structures in materials science.

Injective Modules: Ox-Modules and Injectives

Covers injective modules, Ox-modules, and their relevance in algebraic structures, emphasizing their importance in resolving acyclic resolutions and computing cohomology.