%0 Journal Article %T Characterization of monoids by a generalization of weak flatness property %J Algebraic Structures and Their Applications %I Yazd University %Z 2382-9761 %A Abbasi, Mahdiyeh %A Mohammadzadeh Saany, Hossein %D 2022 %\ 08/09/2022 %V 9 %N 2 %P 57-75 %! Characterization of monoids by a generalization of weak flatness property %K $(WF)'$ %K Condition $(W_{(WF)'})$ %K Condition $(R_{(WF)'})$ %K Condition $(L_{(WF)'})$ %K weakly right reversible %R 10.22034/as.2022.2655 %X In [On a generalization of weak flatness property, Asian-European Journal of Mathematics, 14(1) (2021)] we introduce a generalization of weak flatness property, called $(WF)'$, and showed that a monoid $S$ is absolutely $(WF)'$ if and only if $S$ is regular and satisfies Conditions $(R_{(WF)'})$ and $(L_{(WF)'})$. In this paper we continue the characterization of monoids by this property of their (finitely generated, (mono)cyclic, Rees factor) right acts. Also we give a classification of monoids for which $(WF)'$ property of their (finitely generated, (mono)cyclic, Rees factor) right acts imply other properties and vise versa. The aim of this paper is to show that the class of absolutely $(WF)'$ monoids and absolutely (weakly) flat monids are coincide. %U https://as.yazd.ac.ir/article_2655_557e8ba36783dc32a757b7733ad36f77.pdf