Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Re: Kernel <--> Ideal?

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

    yep!

    as Shredder says!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Kernel <-> Ideal?
  1. Basis of the kernel (Replies: 3)

  2. Kernel Help (Replies: 0)

  3. Kernel and range (Replies: 2)

Loading...