Stability results for projective modules over Rees algebras

We provide a class of commutative Noetherian domains $R$ of dimension $d$ such that every finitely generated projective $R$-module $P$ of rank $d$ splits off a free summand of rank one. On this class, we also show that $P$ is cancellative. At the end we give some applications to the number of generators of a module over the Rees algebras.