1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

First Isomorphism Theorem

  1. Nov 21, 2006 #1
    prove that there does not exist a homomorphism from G:= (integers modulo 8 direct product integers modulo 2) to H:= (intergers modulo 4 direct product integers modulo 4).

    i tried this route, assume that there is such a homomorphism. then by first isomorphism theorem, G/ker phi is isomorphic to phi(G) but what would the kernel of phi have to be in this case?
  2. jcsd
  3. Nov 21, 2006 #2


    User Avatar
    Science Advisor

    Z8 x Z2 => Z4 x Z4??
    There is a homomorphism. For example phi(a, b) = (0, 2b) describes a nontrivial homomorphism, unless I've gone blind.
    Last edited: Nov 21, 2006
  4. Nov 21, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Hrm. Maybe he means to consider them as rings, rather than as additive groups?

    Ring homomorphisms must preserve the identity. (As well as all integer multiples of the identity...)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: First Isomorphism Theorem