Document Type: Original Paper
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Islamic Republic of Iran
Valdis Laan in  introduced an extension of strong flatness which is called weak pullback flatness. In this paper we introduce a new property of acts over monoids, called U-WPF which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. We also show that regularity and strong faithfulness of acts both imply U-WPF. An equivalent of that over monoids for which torsion freeness implies U-WPF is given too.