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Homework Help: Number of elements in a ring with identity.

  1. Mar 12, 2012 #1
    1. The problem statement, all variables and given/known data
    1_R=identity in the ring R.
    /=...not equal
    Having some issues with this any help will be great:
    Let R be a ring with identity, such that
    x^2 = 1_R for all 0_R /= x ,where x belongs to R. How many elements are in R?

    2. Relevant equations

    3. The attempt at a solution
    I'm looking at the element x^2 +1_R which can be = 0 or /=0.
    If it is the first case then x=-1 and where are done |R|=2 because of the powers of x.
    If the latter then (x^2 +1_R)^2=1_R...after calculation this gives x=-1/2 which is false since x^2=1 .
  2. jcsd
  3. Mar 13, 2012 #2
    never mind
    Last edited: Mar 13, 2012
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