On the homological classification of pomonoids: atomic semilattices

Between different and relatively well investigated so-called flatness properties of S-posets there is a property called property (Pw) 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 (Pw) were characterized. In this talk pomonoids which as monoids are atomic semilattices all of whose Rees factor S-posets satisfy property (Pw) will be characterized.