Homological properties of fully bounded Noetherian rings

Abstract

Let R be a fully bounded Noetherian ring of finite global dimension. Then we prove that K dim (R) ≤ gldim(R). If in addition, R is local, in the sense that R/J(R) is simple Artinian, then we prove that R is Auslander-regular and satisfies a version of the Cohen-Macaulay property. As a consequence, we show that a local fully bounded Noetherian ring of finite global dimension is isomorphic to a matrix ring over a local domain, and a maximal order in its simple Artinian quotient ring.