Let R be a ring and S an almost excellent extension of R. We prove that (i)r. f. f. p. D (S) =r. f. f. p. D (R ), r. fpD (S) =r. fpD (R) ; and (ii) if MS is a right S-module then the equality FP-id (MS) =FP-id (MR) holds. We also consider the smash product R # G* and establish similar results.
