Global dimension of factor rings

Abstract

Let R be a right Noetherian ring with right global dimension bounded by 2, which is integral over its centre, and let a be a regular non-unit element in R. Then R/a; R is right hereditary if and only if a; is not in the square of any maximal ideal of R. More generally, we compare for a right Noetherian ring R which is integral over its center, the global dimension of R with the global dimension of R/(a1R + a2R + … + arR) for a regular R-sequence {ai}, which will allow us to give a considerable extension of a result of Hillman.