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.

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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition


Milne, Algebra Course Notes (available free online)


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