\begin{definition}[Definition:Additive Semiring]
An '''additive semiring''' is a semiring with a commutative distributand.
That is, an '''additive semiring''' is a ringoid $\left({S, *, \circ}\right)$ in which:
: $(1): \quad \left({S, *}\right)$ forms a commutative semigroup
: $(2): \quad \left({S, \circ}\right)$ forms a semigroup.
\end{definition}