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- Jun 22, 2012

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In Chapter 2: Ideals on page 32 we find Exercise 2.40 which reads as follows:

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Let I, J be ideals of the commutative ring R such that \(\displaystyle I \subseteq J \).

Show that there is a ring isomorphism

\(\displaystyle \xi \ : (R/I) \ / \ (J/I) \to R/J \)

for which

\(\displaystyle \xi ((r + I) + J/I ) = r + J \) for all \(\displaystyle r \in R\).

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Can someone please help me get started on this exercise.

Also ... problem ... considering J/I ... for a factor ring, J is usually a ring, so what does J/I mean? I assume that since ideals are subgroups under addition, then we can make sense of this by interpreting J/I as a factor group ... Is this the case ... can someone please confirm that my view on this matter is valid ...

As indicated above i would be grateful for some help to get started ...

Peter