Zf. Hao et Wt. Tong, GLOBAL DIMENSION OF RING T=((R)(N) (M)(S)) ((THETA,) (PSI)), Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 38(9), 1995, pp. 1025-1032
Let [GRAPHICS] be a left Noetherian ring, and M a flat right S-module.
It is proved that max {LGD(R), LGD(S)}less than or equal to LGD(T)les
s than or equal to 1+max{LGD(S), 1+pd(N-s)+LGD(R/MN)}.