\begin{definition}[Definition:Ring with Unity]
Let $\struct {R, +, \circ}$ be a non-null ring.
Then $\struct {R, +, \circ}$ is a '''ring with unity''' {{iff}} the multiplicative semigroup $\struct {R, \circ}$ has an identity element.
Such an identity element is known as a unity.
It follows that such a $\struct {R, \circ}$ is a monoid.
\end{definition}