University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 17 4 2006 12 01 On Condition (E?P) - 31777 EN Journal Article In this paper we introduce condition (E?P) a generalization of Conditions (E?), (E) and (P) of acts over monoids and will give a classification of monoids by comparing this condition of their (Rees factor) acts with other properties. We give also a criterion of cyclic acts to satisfy Condition (E?P). https://jsciences.ut.ac.ir/article_31777_9a5a511ca4f18a61719b12acf46f14c0.pdf