# Maximal ideal

1. Oct 22, 2009

### mclove

1. The problem statement, all variables and given/known data

let M be an R-module and I an ideal of R
suppose Mm=0 for all maximal ideals m
then, M=IM

3. The attempt at a solution

O$$\rightarrow$$ IM $$\rightarrow$$ M $$\rightarrow$$ M/IM $$\rightarrow$$ O is exact seq
To show that M/IM=O (then M=IM)

2. Oct 22, 2009

### Petek

Is M a left R-module or a right R-module? You have R operating both on the right (Mm = 0) and the left (M = IM) of M. Also, assuming that all R operations are on the left (say), then what if I is a maximal ideal? We'd then have that M = MI = 0, which doesn't seem correct.

Petek