The authors in 2020 introduced GPW-flatness and gave a characterization of monoids by this property of their right acts
In this article we continue this investigation and will give a characterization of monoids by this condition of their right Rees factor acts. Also we give a characterization of monoids by comparing this property of their right acts with other properties
We also introduce U-GPW-flatness of acts, which is an extension of GPWflatness and give some general properties and a characterization of monoids when this property of acts implies some others and vice versa