On the homological classification of pomonoids by properties of cyclic \(S\)-posets (Q1955586)

Between different so-called flatness properties of \(S\)-posets there is a property \((P_w)\) that is studied here. The author characterizes pomonoids from a subclass of completely simple semigroups with adjoined identity, all of whose cyclic (Rees factor) \(S\)-posets satisfy \((P_w)\). It turns out that in both cases \(S\) is a left group with adjoined identity with certain comparabilities, a non-trivial case being \(L_2\times G\) with adjoined identity, where \(L_2\) is the 2-element left zero semigroup. For the same class of pomonoids necessary and sufficient conditions are given under which all Rees factor \(S\)-posets satisfying property \((P_w)\) satisfy property \((P)\).