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Ring theory question

  1. Oct 17, 2007 #1
    1. The problem statement, all variables and given/known data
    Let R be a commutative ring and a,b in R. Show that the canonical image of ab in R/(f - f^2*g) is idempotent. Give an example where this idempotent is not 0 or 1.


    2. Relevant equations
    None.


    3. The attempt at a solution
    Well I've tried playing with the properties of ideals such as multiplicative closure under R but I've had no luck.
     
  2. jcsd
  3. Oct 18, 2007 #2

    matt grime

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    Surely this will depend on the relationship between a,b and f,g.
     
  4. Oct 18, 2007 #3

    HallsofIvy

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    Please explain what you are talking about! What are f and g? Are they members of R?
     
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