Results 1 to 2 of 2

Math Help - ring homomorphism

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    omaha
    Posts
    8

    ring homomorphism

    Show that the map f : Z9 maps to Z12 defi ned as x maps to 4x is a well de fined ring
    homomorphism. What is the kernel of this map. Find the quotient ring and
    give it's multiplication table.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member jakncoke's Avatar
    Joined
    May 2010
    Posts
    387
    Thanks
    80

    Re: ring homomorphism

    Well definition: Just check if, whenever x = y \in  Z_9 then  \phi(x) = \phi(y) \in Z_{12} Pretty straightforward
    Kernel: What  x \in Z_9 such 4x is divisible by 12, Ker = {0, 3, 6}
    Quotient Ring:  R / Ker(\phi) = \{0 + \{0, 3, 6\}, 1 + \{0, 3, 6\}, 2 + \{0, 3, 6\} \} so 3 elements in the quotient ring.
    Multiplication Table

    --0 1 2

    0 0 0 0

    1 0 1 2

    2 0 2 1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ring homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: March 28th 2010, 03:40 PM
  2. homomorphism ring ~
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 23rd 2009, 10:34 AM
  3. Ring homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 12th 2009, 04:50 AM
  4. Ring Homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 1st 2008, 03:01 PM
  5. Ring Homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 4th 2008, 06:15 PM

Search Tags


/mathhelpforum @mathhelpforum