# Integral Domain

Definition : Let $R$ be a Ring, $R$ is an integral domain if $\forall a,b \in R$ such that $a \neq 0$ and $b \neq 0$ then $a*b \neq 0$

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.