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;) 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.