When principally weakly flat acts satisfy condition (PWP). (Q1434267)

The paper discusses some classes of right \(S\)-acts between the class of pullback flat \(S\)-acts and the class of torsion free \(S\)-acts. The properties considered are: torsion freeness, principal weak flatness, condition (PWP), translation kernel flatness. It is proved, for example, that if \(S\) is a left PP monoid with central idempotents, then all principally weakly flat right Rees factor acts satisfy condition (PWP) if and only if \(S\) is an annihilating chain of right cancellative monoids.