The mathematical term ring is used to designate a type of algebraic system with two compositions satisfying most but not all the properties of addition and multiplication in the system of integers, 0, ±1, ±2, …. In precise terms a ring is a set R with two binary compositions called addition and multiplication whose results on an ordered pair (a,b), a,b in R, are denoted by a + b and ab, respectively. These compositions must satisfy the following conditions: