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Abstract
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Condition (PWP) which was introduced by Laan is related to the concept of flatness of acts over monoids. In this paper, we introduce Condition (PWP)essc which is much easier to check than Condition (PWP) and does not imply it. Also principally weakly flat is a generalization of this condition. At first, general properties of Condition (PWP)essc will be given. Finally
a classification of monoids will be given for which all (cyclic, monocyclic) acts satisfy Condition (PWP)essc.
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