Characterization of monoids by a generalization of weak flatness property

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 , and showed that a monoid is absolutely if and only if is regular and satisfies Conditions and . 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 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 monoids and absolutely (weakly) flat monids are coincide.