# Every class of $S$-acts having a flatness property is closed under directed colimits

Document Type: Research Paper

Authors

1 College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.

2 College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.

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.

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Main Subjects

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### History

• Receive Date: 23 January 2014
• Revise Date: 15 January 2015
• Accept Date: 16 January 2015