Bozkurt, MDurgun, Y2025-04-102025-04-101303-5991http://hdl.handle.net/20.500.14701/37174The concept of subflat domain is used to measure how close (or far away) a module is to be flat. A right module is flat if its subflat domain is the entire class of left modules. In this note, we focus on of RD-flat modules that have subflat domain which is exactly the collection of all torsion-free modules, shortly tf-test modules. Properties of subflat domains and of tf-test modules are studied. New characterizations of left P-coherent rings and torsion-free rings by subflat domains of cyclically presented left R-modules are obtained.EnglishArticle