\section{Definition and Examples}

\begin{definition}[Zero Divisors]
	A \textit{zero-divisor} is a nonzero element $a$ of a commutative ring $R$ such that there is a nonzero element $b \in R$ with $ab = 0$.
\end{definition}

\begin{definition}[Integral Domain]
	An \textit{integral domain} is a commutative ring with unity and no zero-divisors.
\end{definition}

\begin{theorem}[Cancellation]
	Let $a,b$, and $c$ belong to an integral domain If $a \neq 0$ and $ab = ac$, then $b = c$.
\end{theorem}