Classification of monoids by Condition $(PWP_{ssc})$

Condition (PWP) which was introduced in (Laan, V., {it Pullbacks and flatness properties of acts I}, Commun. Algebra, 29(2) (2001), 829-850), is related to flatness concept of acts over monoids. Golchin and Mohammadzadeh in ({it On Condition (PWP_E)}, Southeast Asian Bull. Math., 33 (2009), 245-256) introduced Condition (PWP_E), such that Condition (PWP) implies it, that is, Condition (PWP_E) is a generalization of Condition (PWP). In this paper we introduce Condition (PWP_{ssc}), which is much easier to check  than Conditions (PWP) and (PWP_E) and does not imply them. Also principally weakly flat is a generalization of this condition. At first, general properties of Condition (PWP_{ssc}) will be given. Finally a classification of monoids will be given for which all (cyclic, monocyclic) acts satisfy Condition (PWP_{ssc}) and also a classification of monoids S will be given for which all right S-acts satisfying some other flatness properties have Condition (PWP_{ssc}).