Abstract
In this article, we provide several descriptions of w-coherent rings in terms of modules. We show that a ring R is w-coherent if and only if every direct product of flat modules is w-flat. To do this, we introduce the class of all w-Mittag-Leffler modules with respect to all flat modules and obtain that R is w-coherent if and only if every (finitely generated) ideal is in We also obtain that R is w-coherent if and only if the class of absolutely pure w-modules is closed under direct limits if and only if the class of absolutely pure w-modules is (pre)covering.
Acknowledgement
The authors would like to thank the reviewer for many valuable suggestions on revision of this article.