Proposition 1

a) The ideals $S^{-1}H_{\geq n}$ form an exhaustive and separated filtration of the ring $S^{-1}H$.

b) The canonical homomorphism of $H$ into $S^{-1}H$ induces for each $n$ an isomorphism $u_n$ of $H_n$ onto $S^{-1}H_{\geq n}/S^{-1}H_{\geq n+1}$; the $u_n$ are the homogeneous components of an isomorphism of graded rings of $H$ onto the graded ring associated with $S^{-1}H$, filtered by the $S^{-1}H_{\geq n}$.