@article { author = {Qiao, H. and Wang, L. and Ma, X.}, title = {Every class of $S$-acts having a flatness property is closed under directed colimits}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {42}, number = {2}, pages = {341-351}, year = {2016}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {Let $S$ 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.}, keywords = {Flatness property,colimit,closed}, url = {http://bims.iranjournals.ir/article_764.html}, eprint = {http://bims.iranjournals.ir/article_764_8c92870856f42224b242cd3dc1feb5b5.pdf} }