Summary: Diffusion constants \(D_{R}\) and \(D_{L}\) of ring and linear polymers of the same molecular weight in a good solvent, respectively, have been evaluated through the Brownian dynamics with hydrodynamic interaction in which no bond crossing is possible. The ratio \(C = D_{R}/D_{L}\), which should be universal in the context of the renormalization group, has been estimated as \(C = 1.14 \pm 0.01\) for the large-\(N\) limit. It should be consistent with that of synthetic polymers, while it is smaller than that of DNAs such as \(C\approx \) 1.3. We also perform the same simulation through Brownian dynamics with hydrodynamic interaction where bond crossings are possible, and obtain almost the same estimate for the ratio \(C\).