Global dimension of ring T=(R M N S)_(θ,ψ)

Abstract

Let T=(R M N S) (θ,ψ) be a left Noetherian ring, and M a flat right S-module. It is proved that max {LGD(R), LGD(S)} ≤LGD(T)≤1+max{LGD(S), 1+pd( s N)+LGD(R/MN)}.