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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