Original: Third example : the trivial ring If we define on the singleton set { 0 } : 0 + 0 = 0 0 & times ; 0 = 0 then one can verify that ( { 0 } , + , & times ;/O) forms a ring known as the trivial ring .
Simplified: There exists an element 0 in R , such that for all elements a in R , the equation 0 + a = a + 0 = a holds .