Show that M is an (A/I)-module. Find the submodules.

[peteryellow]

Let A be a ring, I an ideal and M an A-module such that IM=0.
Show that M has a natural structure as an A/I-module and vice versa.
Furthermore show that in the situation above the submodules of M considered
as an A-module or A/I-module are the same.

 

[Hurkyl]

If you aren't going to work on the problem, then neither am I.