\begin{definition}[Definition:Ring (Abstract Algebra)]
A '''ring''' $\struct {R, *, \circ}$ is a semiring in which $\struct {R, *}$ forms an abelian group.
That is, in addition to $\struct {R, *}$ being closed, associative and commutative under $*$, it also has an identity, and each element has an inverse.
\end{definition}