The addition theorem for locally monotileable monoid actions

We prove the so-called Addition Theorem for algebraic entropy of actions cancellative right amenable monoids S on discrete abelian groups A by endomorphisms, under hypothesis that is locally monotileable (that is, admits a Følner sequence (Fn)n?N such Fn monotile Fn+1 every n?N). study in details class groups, also relation with already existing notions monotileability introduced B. Weiss and developed further other authors recently.