- #1

Stephen88

- 61

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## Homework Statement

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?

## Homework Equations

## 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 .