\begin{definition}[Definition:Ringoid (Abstract Algebra)]
A '''ringoid''' is a triple $\struct {S, *, \circ}$ where:
:$S$ is a set
:$*$ and $\circ$ are binary operations on $S$
:the operation $\circ$ distributes over $*$.
That is:
:$\forall a, b, c \in S: a \circ \paren {b * c} = \paren {a \circ b} * \paren {a \circ c}$
:$\forall a, b, c \in S: \paren {a * b} \circ c = \paren {a \circ c} * \paren {b \circ c}$
\end{definition}