\section{Fields}

\begin{definition}[Field]
	A \textit{field} is a commutative ring with unity in which every nonzero element is a unit.
\end{definition}

\begin{theorem}[Finite Integral Domains are Fields]
	A finite integral domain is a field.
\end{theorem}

\begin{corollary}[$\mathbf{\Z_p}$ Is a Field]
	For every prime $p$, $\Z_p$, the ring of integers modulo $p$ is a field.
\end{corollary}