[[Module over a unital associative algebra]]
# Regular representation

The **regular representation** $\Lambda : A \to \End(A)$ of an [[K-monoid]] $A$ is a natural [[Representation]] of $A$ carried by itself, where
$$
\begin{align*}
\Lambda(a)b = a b
\end{align*}
$$
Thus every [[K-monoid]] is a [[Module over a unital associative algebra|module]] ${}_{A}A$ over itself.


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#state/tidy | #lang/en | #SemBr