Abstract
Between different and relatively well investigated so-called flatness properties of S-posets there is a property called property (\({\rm P}_{w}\)) which, so far, has not received much attention. In this paper, we characterize pomonoids from a subclass of completely simple semigroups with adjoined identity all of whose cyclic (Rees factor) S-posets satisfy property (\({\rm P}_{w}\)). Moreover, for the same class of pomonoids, we find necessary and sufficient conditions under which all Rees factor S-posets satisfying property (\({\rm P}_{w}\)) satisfy property (P).
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