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
Since J is an ideal of the ring R, then J itself is a subring of R. So
1) As ...
Ideals of a Ring, Containment and Subgroups are investigated.