Addition Theorem conjecture for algebraic entropy

Let $S$ be a cancellative right amenable monoid acting on the abelian group $A$ on the left by $\alpha$. Let $B$ be an $\alpha$-invariant subgroup of $A$, and write $\alpha_B$ and $\alpha_{A/B}$ for the induced actions on $B$ and $A/B$. Addition Theorem conjecture.

$$h_{alg}(\alpha)=h_{alg}(\alpha_B)+h_{alg}(\alpha_{A/B}).$$

The conjecture is proposed without the hypothesis that $A$ is torsion, extending the addition theorem established in the paper under that hypothesis.