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Math Help - Algebra, Ring theory

  1. #1
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    Algebra, Ring theory

    Does anyone know how to show the following:

    Suppose that R is a ring with identity, and suppose that 1R = 0R. Show that
    R = { 0R }.


    Thx guys.
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  2. #2
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    Quote Originally Posted by suedenation
    Does anyone know how to show the following:

    Suppose that R is a ring with identity, and suppose that 1R = 0R. Show that
    R = { 0R }.


    Thx guys.
    I understand it as,
    1R=0R
    But 0R=\{0\} because 0x=0,\forall x\in R.
    Thus,
    1R=\{0\}.
    Thus,
    But, 1R=R because 1x=x,\forall x\in R.
    Thus,
    R=\{0\}.
    Q.E.D.
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