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Ideals of a Ring : Containment and Subgroups

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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

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Solution Summary

Ideals of a Ring, Containment and Subgroups are investigated.

Solution Preview

Since J is an ideal of the ring R, then J itself is a subring of R. So
1) As ...

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