\begin{definition}[Definition:Regular Representations/Left Regular Representation]
Let $\struct {S, \circ}$ be a magma.
The mapping $\lambda_a: S \to S$ is defined as:
:$\forall x \in S: \map {\lambda_a} x = a \circ x$
This is known as the '''left regular representation of $\struct {S, \circ}$ with respect to $a$'''.
\end{definition}