Published online by Cambridge University Press: 18 May 2009
In the study of idealizer rings in [14], the global dimensions of certain subrings were calculated. This work was extended by Goodearl [9]. Here it is shown, in Section 1, that the techniques involved can be used rather more generally than was apparent there. The results concern a ring S with a right ideal A such that SA = S, and a subring R of S containing A. They describe gl dim R in terms of gl dim S and the projective dimensions of simple subfactors of S/R or R/A, provided that these R-modules are sufficiently well conditioned.