Results 1 to 2 of 2

Thread: Isomorphism between R/R and {0}

  1. February 3rd 2011, 09:07 AM #1
    Ginsburg
    Ginsburg is offline
    Newbie
    Joined
    Jul 2010
    Posts
    8

    Isomorphism between R/R and {0}

    if R is a ring, why is there an isomorphism between R/R and {0}?
    I don't understand how is it even possible because R/R = R.
    Thanks.
    Follow Math Help Forum on Facebook and Google+
  2. February 3rd 2011, 09:29 AM #2
    FernandoRevilla
    FernandoRevilla is offline
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,154
    Thanks
    38
    [x],[y]\in R/R

    are equal iff

    x-y\in R

    This happen for all x,y\in R so, R/R has only one element:

    R/R=\{[0]\}


    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+
« Projections | Find |X| such that |X| is not 0, and is not divisible by a prime p in N »

Similar Math Help Forum Discussions

  1. Isomorphism
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: October 27th 2010, 12:08 AM
  2. isomorphism
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 30th 2010, 09:52 AM
  3. isomorphism
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 10th 2010, 08:50 AM
  4. Isomorphism proves: f and g are isomorphisms, prove f + g is an isomorphism
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: February 14th 2010, 03:05 AM
  5. Isomorphism
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: June 28th 2009, 11:13 PM

Search Tags


/mathhelpforum @mathhelpforum