Hermite and ps-rings of hurwitz series ∗

Let R be a commutative ring and H R the ring of Hurwitz series over R. In this note, we consider some properties of rings, which are shared by R and HR. In particular, we show that for the rings R and H R, if either ring is (i) a Hermite ring, or (ii) a PF-ring in the sense that every finitely generated projective R-module is free, then so is another. We also show that if R is a PS-ring in the sense that the socle Soc( _RR) is projective and char(R) = 0, then H R is also a PS-ring.