Let R be a ring and M an R-module. Then M is said to be regular w-flat provided that the natural homomorphism I circle times(R) M -> R circle times(R) M is a w-monomorphism for any regular ideal I. We distinguish regular w-flat modules from regular flat modules and w-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Prufer v-multiplication rings (PvMRs for short) utilizing the homological properties of regular w-flat modules.
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