Refail AlizadeYılmaz DurǧunAlizade, RafailDurğun, Yılmaz2025-10-06201700418994, 224029260041-89942240-292610.4171/RSMUP/137-42-s2.0-85019582285https://www.scopus.com/inward/record.uri?eid=2-s2.0-85019582285&doi=10.4171%2FRSMUP%2F137-4&partnerID=40&md5=d537618a9b07afef50da4bd43b041466https://gcris.yasar.edu.tr/handle/123456789/9728https://doi.org/10.4171/RSMUP/137-4A 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(M N) = 0 implies N is flat. f-test modules are a flat version of the Whitehead test modules for injectivity defined 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 (finitely 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. © 2023 Elsevier B.V. All rights reserved.Englishinfo:eu-repo/semantics/closedAccessF-test Modules, Flat Modules, Fully Saturated Rings, P-indigent Modules, Whitehead Test ModulesFlat ModulesFully Saturated RingsP-Indigent ModulesF-Test ModulesWhitehead Test ModulesArticle