How do I find all objects $X$ such that $\operatorname{Hom}(-,X)$ is an abelian group in the category $\mathcal{Alg}_{R/A}$ of algebras over a fixed $R-$algebra $A$?
I have been considering what being over $A$ induces, but am making no progress right now. The claim is that they are all of the form $A\ltimes M$ for $M$ an $A-$module.