An Additive Subgroup (I,+) of a Ring where: ∀r∈R,∃x∈I,rx∈I Showing Ideals Show non-empty Show that ∀r∈R,∃x∈I,rx∈I Concepts Generator for Ideal Trivial Ideal Generator for Ideal Intersection Generator for Ideal Sum Examples Showing Even Integers are a Ideal Let x∈{even numbers},x=2k,k∈Z Let r∈Z, then ,rx=r(2k)=2(rk) Thus, rx∈{even numbers}