Let R be a commutative integral domain with 1 and Q its field of quotients. We show that if p.d.$\sb{\rm R}$ Q = 1, then Q/R is a direct sum of countably generated R-modules. We also show that any divisible torsion module of projective dimension one over R with p.d.$\sb{\rm R}$ Q = 1 is a direct sum of countably generated R-modules. These give us two characterizations of domains R with p.d.$\sb{\rm R}$ Q = 1. We find a classification theorem of divisible modules of projective dimension one over R with p.d.$\sb{\rm R}$ Q = 1. We show that countably generated torsion-free modules over valuation domains R with p.d.$\sb{\rm R}$ Q $>$ 1 can be embedded in free R-modules and generalize this to uncountably generated torsion-free modules