Regular representation

The regular representation $Λ : 𝐴 \to E n d (𝐴)$ of an K-monoid $𝐴$ is a natural Representation of $𝐴$ carried by itself, where

Λ (𝑎) 𝑏 = 𝑎 𝑏

Thus every K-monoid is a module $𝐴 𝐴$ over itself.