Abstract: Let R1,R2,…,Rm be rings.It is  proved that (1) mi=1Ri is a right (n,d)-ring (resp. weak (n,d)-ring,n-coherent ring) if and only if each Ri is a right (n,d)-ring (resp. weak (n,d)-ring,n-coherent ring);(2) rD（mi=1Ri) =sup{rD(R1),rD(R2),…,rD(Rm)};(3)  wD(mi=1Ri) = sup{wD(R1),wD(R2),…,wD(Rm)}.

Key words: (weak) (n,d)-ring, (n,d)-injective module, (n,d)-flat module, n-presented module, n-coherent ring, (weak) global dimension