  For a unital ring, it is an open question whether flatness of simple modules
implies all modules are flat and thus the ring is von Neumann regular. The
question was raised by Ramamurthi over 40 years ago who called such rings
SF-rings (i.e., simple modules are flat). In this note we show that a SF
Steinberg algebra of an ample Hausdorff groupoid, graded by an ordered group,
has an aperiodic unit space. For graph groupoids this implies that the graphs
are acyclic. Combining with the Abrams-Rangaswamy Theorem, it follows that SF
Leavitt path algebras are regular, answering Ramamurthi's question in positive
for the class of Leavitt path algebras.
