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Ideals in Ring Theory (Abstract Algebra)

An ideal of a ring is the similar to a normal subgroup of a group. Using an ideal, you can partition a ring into cosets, and these cosets form a new ring - a "factor ring." (Also called a "quotient ring.") After reviewing normal subgroups, we will show you why the definition of an ideal is the simplest one that allows you to create factor rings. As an example, we will look at an ideal of the ring Z[x], the ring of polynomials with integer coefficients. ♦♦♦♦♦♦♦♦♦♦ This video was made possible by our VIP Patrons on Patreon! Thank you for supporting our work this year. Because of you, we are able to continue making the highest quality math videos, free for the world. Our amazingly generous Patrons include Tracy Karin Prell, Carlos Araujo, Markie Waid, Martin Stephens, David Borger, Burhan Saifaddin, MdeG, Michael, Umar Khan, John Krawiec, Patrick Cool, Tim Tapio, Deeptanshu Malik, Kevin B, Terrill Frantz, Charles Southerland, Andre Gibbs, and Ahmed Sakr. ► 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 #AbstractAlgebra #Math #Maths ♦♦♦♦♦♦♦♦♦♦