It is proved that every commutative ring whose RD-injective modules are Σ-RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian (respectively simple) module is RD-injective, is given. These results can be obtained by using the properties of RD-flat modules and RD-coflat modules which are respectively th...

In this paper, we introduce and study the class [Formula: see text]-[Formula: text]-ML of text]-Mittag-Leffler modules with respect to all flat modules. We show that a ring text] is text]-coherent if only every ideal in text]-ML, closed under submodules. As an application, obtain text]-version Chase Theorem: any direct product copies text]-flat, text]-modules text]-flat. Consequently, provide a...