Definition of an Integral Domain

If we have a commutative ring with unity $R$, then $R$ is an integral domain if it has no zero divisors (e.g. $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$, and $\mathbb{C}$):

• Commutative,
• Unity is $1$,
• $a\cdot b=0⟺a=0\text{ or }b=0$.