Thread: Ideal

Let R be a commutative ring with ideals I,J such that I ⊆J ⊆R. Show that J/I is an ideal of R/I.

I am not sure how to begin. Thanks in advance for any help.

Originally Posted by page929

Let R be a commutative ring with ideals I,J such that I ⊆J ⊆R. Show that J/I is an ideal of R/I.

I am not sure how to begin. Thanks in advance for any help.

Prove that is an additive subgroup of and that

Tonio

You do know what means, right? I've seen some people get stuck with this simply from not knowing what is meant by "an ideal mod an ideal".

I don't think that I do. Can you explain it to me?

As a set, . They're the cosets in whose representatives come from . Notice that it makes sense to discuss this since .