On characterizations ofw-coherent rings

摘要

In this article, we provide several descriptions ofw-coherent rings in terms of modules. We show that a ringRisw-coherent if and only if every direct product of flat modules isw-flat. To do this, we introduce the classw-F-MLof allw-Mittag-Leffler modules with respect to all flat modules and obtain thatRisw-coherent if and only if every (finitely generated) ideal is inw-F-ML.We also obtain thatRisw-coherent if and only if the class of absolutely purew-modules is closed under direct limits if and only if the class of absolutely purew-modules is (pre)covering.