New Characterizations of S-coherent rings
Abstract
In this paper, we introduce and study the class S-F-ML of S-Mittag-Leffler modules with respect to all flat modules. We show that a ring R is S-coherent if and only if S-F-ML is closed under submodules. As an application, we obtain the S-version of Chase Theorem: a ring R is S-coherent if and only if any direct product of R is S-flat if and only if any direct product of flat R-modules is S-flat. Consequently, we provide an answer to the open question proposed by D. Bennis and M. El Hajoui [3].
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