Abstract
In this paper, we introduce and study the class [Formula: see text]-[Formula: see text]-ML of [Formula: see text]-Mittag-Leffler modules with respect to all flat modules. We show that a ring [Formula: see text] is [Formula: see text]-coherent if and only if every ideal is in [Formula: see text]-[Formula: see text]-ML, if and only if [Formula: see text]-[Formula: see text]-ML is closed under submodules. As an application, we obtain the [Formula: see text]-version of Chase Theorem: a ring [Formula: see text] is [Formula: see text]-coherent if and only if any direct product of copies of [Formula: see text] is [Formula: see text]-flat, if and only if any direct product of flat [Formula: see text]-modules is [Formula: see text]-flat. Consequently, we provide an answer to the open question proposed by Bennis and El Hajoui [On [Formula: see text]-coherence, J. Korean Math. Soc. 55(6) (2018) 1499–1512].
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