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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