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Maximal ideal

  1. Oct 22, 2009 #1
    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[tex]\rightarrow[/tex] IM [tex]\rightarrow[/tex] M [tex]\rightarrow[/tex] M/IM [tex]\rightarrow[/tex] O is exact seq
    To show that M/IM=O (then M=IM)
  2. jcsd
  3. Oct 22, 2009 #2
    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.

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