A ring is a commutative group under addition that has a second operation: multiplication. These generalize a wide variety of mathematical objects like the integers, polynomials, matrices, modular arithmetic, and more. In this video we will take an in depth look at the definition of a ring.

Our Abstract Algebra playlist is here:
http://bit.ly/AbstractAlgebraSocratica

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

♦♦♦♦♦♦♦♦♦♦

This video was made possible by the generous support of our Patrons on Patreon! We'd like to recognize the outstanding help from our VIP Patrons: Tracy Karin Prell, Carlos Araujo, Markie Waid, Martin Stephens, David Borger, Burhan Saifaddin, Cadmus, MdeG, Michael, Richard M Haynes, Umar Khan, John Krawiec, Timothy Tapio, Samuel Ytterbrink, and Patrick Cool.
Ways to support our channel:

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

Thank you!

♦♦♦♦♦♦♦♦♦♦

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...

♦♦♦♦♦♦♦♦♦♦

Connect with us!

Facebook:   / socraticastudios  
Instagram:   / socraticastudios  
Twitter:   / socratica  

♦♦♦♦♦♦♦♦♦♦

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

♦♦♦♦♦♦♦♦♦♦