Unique homomorphic extension theorem
The unique homomorphic extension theorem is a result in mathematical logic which formalizes the intuition that the truth or falsity of a statement can be deduced from the truth values of its parts. (Wikipedia).
The unique homomorphic extension theorem is a result in mathematical logic which formalizes the intuition that the truth or falsity of a statement can be deduced from the truth values of its parts. (Wikipedia).
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Chapter 6: Homomorphism and (first) isomorphism theorem | Essence of Group Theory
The isomorphism theorem is a very useful theorem when it comes to proving novel relationships in group theory, as well as proving something is a normal subgroup. But not many people can understand it intuitively and remember it just as a kind of algebraic coincidence. This video is about t
From playlist Essence of Group Theory
Group Homomorphisms and the big Homomorphism Theorem
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra
Homomorphisms in abstract algebra examples
Yesterday we took a look at the definition of a homomorphism. In today's lecture I want to show you a couple of example of homomorphisms. One example gives us a group, but I take the time to prove that it is a group just to remind ourselves of the properties of a group. In this video th
From playlist Abstract algebra
Introduction to additive combinatorics lecture 5.8 --- Freiman homomorphisms and isomorphisms.
The notion of a Freiman homomorphism and the closely related notion of a Freiman isomorphism are fundamental concepts in additive combinatorics. Here I explain what they are and prove a lemma that states that a subset A of F_p^N such that kA - kA is not too large is "k-isomorphic" to a sub
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra
Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory
Lecture 34. Galois groups and fixed fields
From playlist Abstract Algebra 2
What is a Group Homomorphism? Definition and Example (Abstract Algebra)
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From playlist Abstract Algebra
Christopher Schafhauser: "Non-stable extension theory and the classification of C∗-algebras"
Actions of Tensor Categories on C*-algebras 2021 "Non-stable extension theory and the classification of C∗-algebras" Christopher Schafhauser - University of Nebraska-Lincoln Abstract: Over the last decade, much of the progress in the classification and regularity theory of simple, nuclea
From playlist Actions of Tensor Categories on C*-algebras 2021
José Carrión: "The abstract approach to classifying C*-algebras"
Actions of Tensor Categories on C*-algebras 2021 Mini Course: "The abstract approach to classifying C*-algebras" José Carrión - Texas Christian University Institute for Pure and Applied Mathematics, UCLA January 21, 2021 For more information: https://www.ipam.ucla.edu/atc2021
From playlist Actions of Tensor Categories on C*-algebras 2021
Surjective homomorphisms in abstract algebra
We have looked at homomorphisms before: https://www.youtube.com/watch?v=uTIvIFmVEAg&list=PLsu0TcgLDUiI2VH4ubaKNLxp8O5DN9pF3&index=33 https://www.youtube.com/watch?v=NuYczPkUZGY&list=PLsu0TcgLDUiI2VH4ubaKNLxp8O5DN9pF3&index=34 https://www.youtube.com/watch?v=3Oo0O1vVPoQ&list=PLsu0TcgLDUiI2V
From playlist Abstract algebra
Gregory Henselman-Petrusek (9/28/22): Saecular persistence
Homology with field coefficients has become a mainstay of modern TDA, thanks in part to structure theorems which decompose the corresponding persistence modules. This naturally begs the question -- what of integer coefficients? Or homotopy? We introduce saecular persistence, a categoric
From playlist AATRN 2022
Galois Representations 2 by Shaunak Deo
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
Christopher Schafhauser: On the classification of nuclear simple C*-algebras, Lecture 4
Mini course of the conference YMC*A, August 2021, University of Münster. Abstract: A conjecture of George Elliott dating back to the early 1990’s asks if separable, simple, nuclear C*-algebras are determined up to isomorphism by their K-theoretic and tracial data. Restricting to purely i
From playlist YMC*A 2021
Elliptic Curves - Lecture 10b - Isogenies (part 2)
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Lecture 30. Fields, field extensions
0:00 Fields 1:48 Examples of fields 08:20 Characteristic of a field 11:20 Prime subfields (Q, F_p) 12:00 Every field has a prime subfield; relation of prime subfield to characteristic 20:15 Frobenius homomorphism 22:40 Field extension 23:50 A field extension of K possesses a structure of
From playlist Abstract Algebra 2
Group Homomorphisms - Abstract Algebra
A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another. Homomorphisms will be
From playlist Abstract Algebra