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 every ideal is in S -F-ML, 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 copies 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 Bennis and El Hajoui.
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