On a Conjecture on the weak global dimension of Gaussian rings

Abstract

Bazzoni and Glaz conjecture that the weak global dimension of a Gaussian ring is 0,1 or \infty. In this paper, we prove their conjecture in all cases except when R is a non-reduced local Gaussian ring with nilradical $\mathcal{N} satisfying $\mathcal{N}^2=0$.