On characterizations of <i>w</i>-coherent rings

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 w‐F‐ML 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 w‐F‐ML. 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.

Topics & Concepts