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I assume that x_2 = 1_R should read $x^2 = 1_R$.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?
Thanks
if (x+1_r)^2=1_r =>x=-1/2...but x^2=1 so this is a contradiction....therefore x=-1=>|R|=2(because of the powers of x).Correct?that is, i believe, what Opalg was hinting at.