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Kernel <-> Ideal?

  1. Feb 10, 2009 #1
    Kernel <--> Ideal?

    I know that all kernels of ring homomorphisms are ideals, but is it true that for any ideal I of a ring R, there exists a homomorphism f: R -> R' such that Ker(f)=I?
  2. jcsd
  3. Feb 10, 2009 #2


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    Re: Kernel <--> Ideal?

    You map R to R/I by x->xI
  4. Feb 12, 2009 #3
    Re: Kernel <--> Ideal?


    as Shredder says!
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