\begin{definition}[Definition:Irreducible Element of Ring/Definition 2]
Let $\struct {D, +, \circ}$ be an integral domain whose zero is $0_D$.
Let $\struct {U_D, \circ}$ be the group of units of $\struct {D, +, \circ}$.
Let $x \in D: x \notin U_D, x \ne 0_D$, that is, $x$ is non-zero and not a unit.
$x$ is defined as '''irreducible''' {{iff}} the only divisors of $x$ are its associates and the units of $D$.
That is, {{iff}} $x$ has no proper divisors.
\end{definition}