Uploaded February 2020 | Updated September 2026, 3 weeks ago

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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.

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

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

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

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