  This paper deals with well-known notion of $PF$-rings, that is, rings in
which principal ideals are flat.
  We give a new characterization of $PF$-rings. Also, we provide a necessary
and sufficient condition for $R\bowtie I$ (resp., $R/I$ when $R$ is a Dedekind
domain or $I$ is a primary ideal) to be $PF$-ring. The article includes a brief
discussion of the scope and precision of our results.
