An Introduction to Homological Algebra
《An Introduction to Homological Algebra》 · 第 456、459 页 · Chapter 8, Section 8.1, Definitions
If \(R\) is a ring, then its left projective global dimension is \({}^{\ell}\operatorname{pD}(R)=\sup\{\operatorname{pd}(A):A\in\operatorname{obj}(R\text{-}\mathbf{Mod})\}\). […] If \(R\) is a ring, then its left global dimension \({}^{\ell}\operatorname{D}(R)\) is the common value of \({}^{\ell}\operatorname{pD}(R)\) and \({}^{\ell}\operatorname{iD}(R)\).