### Ideals of a Ring : Containment and Subgroups

Let J and I be ideals of the ring R, with J C I C R. Show that J is an ideal in the ring I (Recall that any ideal of a ring is also a subring; so I is a ring in its own right) Note that: To show J an ideal of I, we must show that 1) it is an additive subgroup of R and 2) it is satisfied bJ C J and Jb C J