 A commutative ring is an algebraic structure where addition, subtraction and multiplication are defined.The integers are a ring, and the prime numbers in the integers have been generalized to rings in two different ways, "prime elements" and "irreducible elements".An element formula_20 of a ring formula_175 is called prime if it is nonzero, has no multiplicative inverse (that is, it is not a unit), and satisfies the following requirement