Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40320140601When every $P$-flat ideal is flat677688enFatima CheniourDepartment of Mathematics, FST, University of FezNajib MahdouDepartment of Mathematics, Faculty of Sciences and Technology, University of Fez, Fez, Morocco.201301131$ and of non-$PFF$ Pr"{u}fer-ring. Also, we investigate the stability of this property under localization and homomorphic image, and its transfer to finite direct products. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.]]>http://bims.iranjournals.ir/pdf_523_d6d550a815d948c112a45d8e9bbc1778.html