  We prove an instance of the so-called Addition Theorem for the algebraic
entropy of actions of cancellative right amenable monoids $S$ on discrete
abelian groups $A$ by endomorphisms, under the hypothesis that $S$ is locally
monotileable (that is, $S$ admits a right F\o lner sequence $(F_n)_{n\in\mathbb
N}$ such that $F_n$ is a monotile of $F_{n+1}$ for every $n\in\mathbb N$). We
study in details the class of locally monotileable groups, also in relation
with already existing notions of monotileability for groups, introduced by
Weiss and developed further by other authors recently.
