Third example : the trivial ring If we define on the singleton set -LCB- NUMBER@1 -RCB- : NUMBER@1 + NUMBER@1 = NUMBER@1 NUMBER@1 & times ; NUMBER@1 = NUMBER@1 then one can verify that -LRB- -LCB- NUMBER@1 -RCB- , + , & times ;-RRB- forms a ring known as the trivial ring .

There exists an element NUMBER@1 in R , such that for all elements a in R , the equation NUMBER@1 + a = a + NUMBER@1 = a holds .
