Maximal ideal

  • Thread starter mclove
  • Start date
  • #1
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Homework Statement



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




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)
 

Answers and Replies

  • #2
Petek
Gold Member
365
9
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
 

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