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.(Thinking) Thanks in advance for any help.

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- March 8th 2011, 04:42 AMpage929Ideal
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.(Thinking) Thanks in advance for any help. - March 8th 2011, 05:37 AMtonio
- March 8th 2011, 07:12 AMtopspin1617
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".

- March 8th 2011, 08:59 AMpage929
I don't think that I do. Can you explain it to me?

- March 8th 2011, 12:50 PMtopspin1617
As a set, . They're the cosets in whose representatives come from . Notice that it makes sense to discuss this since .