Frame coreflection of a preframe monoid ($R(M)=\{x:e\le x,x\ast x=x\}$)

For a commutative monoid object $(M,\ast ,e)$ in preframes, the indicated subset is a frame. Its bottom is $e$, its binary join is $\ast$, and its directed joins and finite meets are inherited. Every homomorphism from a frame regarded as a join monoid factors uniquely through this subset. This gives a coreflective subcategory.