Kernels of Homomorphisms | Abstract Algebra
5.9 هزار بار بازدید -
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We introduce kernels of homomorphisms.
We introduce kernels of homomorphisms. We give the definition of kernel in group theory, an example of a kernel of a homomorphism onto the additive group of real numbers, then finish by proving the kernel of a homomorphism is a normal subgroup of the domain group of the homomorphism. #abstractalgebra #grouptheory
Abstract Algebra Course: Abstract Algebra
Abstract Algebra Exercises: Abstract Algebra Exercises
Group Homomorphisms: Intro to Group Homomorphisms | Abstra...
Basic Properties of Homomorphisms: Proof: Basic Properties of Homomorphi...
Normal Subgroups: Definition of Normal Subgroups | Abst...
Fundamental Homomorphism Theorem: (coming soon)
0:00 - Intro
0:33 - Definition of Kernel of a Homomorphism
1:26 - Example of a Kernel of a Homomorphism
5:08 - Proof Kernel is a Normal Subgroup
10:21 - Outro
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Abstract Algebra Course: Abstract Algebra
Abstract Algebra Exercises: Abstract Algebra Exercises
Group Homomorphisms: Intro to Group Homomorphisms | Abstra...
Basic Properties of Homomorphisms: Proof: Basic Properties of Homomorphi...
Normal Subgroups: Definition of Normal Subgroups | Abst...
Fundamental Homomorphism Theorem: (coming soon)
0:00 - Intro
0:33 - Definition of Kernel of a Homomorphism
1:26 - Example of a Kernel of a Homomorphism
5:08 - Proof Kernel is a Normal Subgroup
10:21 - Outro
◉Textbooks I Like◉
Graph Theory: https://amzn.to/3JHQtZj
Real Analysis: https://amzn.to/3CMdgjI
Proofs and Set Theory: https://amzn.to/367VBXP (available for free online)
Statistics: https://amzn.to/3tsaEER
Abstract Algebra: https://amzn.to/3IjoZaO
Discrete Math: https://amzn.to/3qfhoUn
Number Theory: https://amzn.to/3JqpOQd
★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: Patreon: wrathofmathlessons
◆ Donate on PayPal: https://www.paypal.me/wrathofmath
Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon!
Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/
Follow Wrath of Math on...
● Instagram: Instagram: wrathofmathedu
● Facebook: Facebook: WrathofMath
● Twitter: Twitter: wrathofmathedu
My Math Rap channel: @mathbars2020
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