Fund Project:Research supported by National Natural Science Foundation of China (10171082)and by the Teaching and Research Award Program for Outstanding Young Teach ers in Higher Education Institutions of MOE.
Let R, S be rings, U a flat right .R-rnodule and V a flat right S-module. We show in this paper that (N, (U, V))-lc.dim(R⊕S) = sup((N, U)-lc.dimR, (N, V)-lc.dimS).