# Ideals in Rings

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.

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.