Let R be a ring.
Show that the following are equivaltent:
i) The characteristic of R is 2, i.e., for all elements x of R, 2x = x + x = 0.
X+X=0
ADDING X ON BOTH SIDES AS R IS A RNG, WE GET
0-X=X+X-X
-X=X
SO THIS STATEMENTS IS EQUIVALENT TO STATEMENT ii
ii) For all x
R, -x = x.
WE HAVE
-X=X
ADDING X ON BOTH SIDES AS R IS A RNG, WE GET
-X+X=X+X
0=X+X
SO THIS STATEMENTS IS EQUIVALENT TO STATEMENT i