Rafail AlizadeYilmaz Durgun2025-10-0620170041-89942240-292610.4171/RSMUP/137-4http://dx.doi.org/10.4171/RSMUP/137-4https://gcris.yasar.edu.tr/handle/123456789/7163A right R-module M is said to be a test module for flatness (shortly: an f-test module) provided for each left R-module N Tor(MN) = 0 implies N is flat. f-test modules are a flat version of the Whitehead test modules for injectivity deflned by Trlifaj. In this paper the properties of f-test modules are investigated and are used to characterize various families of rings. The structure of a ring over which every (flnitely generated) right R-module is flat or f-test is investigated. Abelian groups that are Whitehead test modules for injectivity or f-test are characterized.EnglishWhitehead test modules, f-test modules, p-indigent modules, flat modules, fully saturated ringsArticle