Lectures related to Local Rings and Residues

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Local structure of totally disconnected locally compact groups III

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Ideal Class Group Relations

Covers the relations between the ideal class group and proper fractional ideals.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Ideals and Representations Log in to Mediaspace to watch this video

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

Hilberts Nullstellensatz and Ideals Log in to Mediaspace to watch this video

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

Principal Ideal Domains: Structure and Homomorphisms Log in to Mediaspace to watch this video

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Simple Modules: Schur's Lemma Log in to Mediaspace to watch this video

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

Chinese Remainder Theorem: Rings and Fields Log in to Mediaspace to watch this video

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Dedekind Rings and Fractional Ideals Log in to Mediaspace to watch this video

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

Dimension Theory of Rings Log in to Mediaspace to watch this video

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

Algebraic Geometry: Localization and Prime Ideals Log in to Mediaspace to watch this video

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