Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Every class of $S$-acts having a flatness property is closed under directed colimits341351764ENH.QiaoCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.L.WangCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.X.MaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.Journal Article20140123Let $S$ be a monoid. In this paper, we prove every class of $S$-acts having a flatness property is closed underdirected colimits, it extends some known results. Furthermore this result implies that every $S$-act has a flatness cover if and only if it has a flatness precover.http://bims.iranjournals.ir/article_764_8c92870856f42224b242cd3dc1feb5b5.pdf