Let R be a commutative ring. An R-module M is said to be an absolutely w-pure module if Ext(R)(1)(F, M) is GV-torsion for any finitely presented R-module F. In this paper, we further study some homological properties of absolutely w-pure modules and introduce the weak FP-injective dimension. The closeness of some classes of absolutely w-pure modules is discussed. By comparing, we also give examples to show that the class of absolutely w-pure modules is not necessarily closed under the intersection of a descending chain of absolutely w-pure modules or under the submodules of absolutely w-pure modules. Finally, the weak FP-injective dimension over coherent rings is studied.
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