The Kernel of a Group Homomorphism – Abstract Algebra

Socratica منتشر شده در تاریخ 1395/02/13

282.7 هزار بار بازدید - 8 سال پیش - The kernel of a group

The kernel of a group homomorphism measures how far off it is from being one-to-one (an injection). Suppose you have a group homomorphism f:G → H. The kernel is the set of all elements in G which map to the identity element in H. It is a subgroup in G and it depends on f. Different homomorphisms between G and H can give different kernels.

If f is an isomorphism, then the kernel will simply be the identity element.

You can also define a kernel for a homomorphism between other objects in abstract algebra: rings, fields, vector spaces, modules. We will cover these in separate videos.

Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W

♦♦♦♦♦♦♦♦♦♦

We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/2oOBd5S

Milne, Algebra Course Notes (available free online)
http://www.jmilne.org/math/CourseNote...

♦♦♦♦♦♦♦♦♦♦

Ways to support our channel:

► Join our Patreon : Patreon: socratica
► Make a one-time PayPal donation: https://www.paypal.me/socratica
► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9

Thank you!

♦♦♦♦♦♦♦♦♦♦

Connect with us!

Facebook: Facebook: SocraticaStudios
Instagram: Instagram: SocraticaStudios
Twitter: Twitter: Socratica

♦♦♦♦♦♦♦♦♦♦

Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison

♦♦♦♦♦♦♦♦♦♦

8 سال پیش در تاریخ 1395/02/13 منتشر شده است.

282,776 بـار بازدید شده

... بیشتر