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
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
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
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
Homomorphisms (Abstract Algebra)
A homomorphism is a function between two groups. It's a way to compare two groups for structural similarities. Homomorphisms are a powerful tool for studying and cataloging groups. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ W
From playlist Abstract Algebra
302.3A: Review of Homomorphisms
A visit to the homomorphism "zoo," including definitions of mono-, epi-, iso-, endo-, and automorphisms.
From playlist Modern Algebra - Chapter 17 (group homomorphisms)
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
Group Homomorphisms and the big Homomorphism Theorem
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra
Schemes 10: Morphisms of affine schemes
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We try to define morphisms of schemes. The obvious definition as morphisms of ringed spaces fails as we show in an example. Instead we have to use the more su
From playlist Algebraic geometry II: Schemes
Stability and sofic approximations for product groups and property (tau) - Adrian Ioana
Stability and Testability Topic: Stability and sofic approximations for product groups and property (tau) Speaker: Adrian Ioana Affiliation: University of California, San Diego Date: November 4, 2020 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem The fundamental homomorphism theorem (FHT), also called the "first isomorphism theorem", says that the quotient of a domain by the kernel of a homomorphism is isomorphic to the image. We motivate this with Cayley diagr
From playlist Visual Group Theory
What is a Group Homomorphism? Definition and Example (Abstract Algebra)
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys What is a Group Homomorphism? Definition and Example (Abstract Algebra)
From playlist Abstract Algebra
EDIT: At 8:35, should use q instead of pi. Abstract Algebra: We define homomorphism between groups and draw connections to normal subgroups and quotient groups. Precisely the kernel of a homomorphism is a normal subgroup, and we can associate a surjective homomorphism to every normal
From playlist Abstract Algebra
Asymptotic Bounded Cohomology and Uniform Stability of high-rank lattices - Bharatram Rangarajan
Arithmetic Groups Topic: Asymptotic Bounded Cohomology and Uniform Stability of high-rank lattices Speaker: Bharatram Rangarajan Affiliation: Hebrew University Date: March 16, 2022 In ongoing joint work with Glebsky, Lubotzky, and Monod, we construct an analog of bounded cohomology in an
From playlist Mathematics
From playlist Abstract Algebra 2
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)
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplicat
From playlist Visual Group Theory
Homomorphisms and Isomorphisms -- Abstract Algebra 8
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From playlist Abstract Algebra