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Commutative ring with unit

  1. Sep 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Given a set R={x,y,a,b}

    There are 2 tables shown: one is the addition of x,y,a,b elements with x,y,a,b elements. The 2nd table is multiplication of each element with the other elements. (The 2nd table shows that x multiplied by anything equals x)

    we have a+b=y and (a)(b)=y

    Decide which elements must be the 0 and the 1, then prove that this is a commutative ring with unit.

    3. The attempt at a solution
    I know how to show it is commutative. I'm just having trouble starting on it.

    Well if the addition of a and b equals the multiplication of a and b, then a=b=y=0. Is this right? But then since x multiplied by anything equals x, then x must also be 0. But then there is no element 1. So how can I show commutativity with this??

    Also don't know how to show that there exists units.
    Last edited: Sep 7, 2008
  2. jcsd
  3. Sep 8, 2008 #2


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