\begin{definition}[Definition:Rng]
In the context of abstract algebra, a '''rng''' is a ring $\struct {R, +, \circ}$ which specifically does not have a unity.
That is, such that the semigroup $\struct {R, \circ}$ does not have an identity element.
The name arises from its nature as a r'''i'''ng with no '''i'''dentity element.
\end{definition}