On the homological classification of pomonoids: atomic posemilattices

Between dierent and relatively well investigated so-called flatness properties of S -posets there is a property called property (P w ) which, so far, has not received much attention. In a recent paper by the author pomonoids from a subclass of completely simple semigroups with adjoined identity, all of whose cyclic (Rees factor) S -posets satisfy property (P w ), were characterized. In this paper pomonoids which as monoids are atomic semilattices, all of whose Rees factor S -posets satisfy property (P w ), are characterized.