**Definition :** Let be a Ring, is an integral domain if such that and then

An integral domain is a Ring where no two nonzero elements can produce zero when multiplied. Thus integral domains do not have zero divisors. One can show that a Ring is an integral domain by showing the existence of units. An example of an integral domain is the integers since no two nonzero integer can produce zero through multiplication.

**See Also :** Ring, Unit, Zero Divisor