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Math Help - Isomorphism between R/R and {0}

  1. #1
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    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.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    45
    [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
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