On dominant dimension of Noetherian rings
If each of the first n terms of the minimal injective resolution of an R- module M is flat, then M is said to have dominant dimension at least n, dom.dim(M)\(\geq n\). A ring R with \(dom.\dim (R_ R)\geq 1\) is called right QF-3, and \textit{K. Morita} [Proc. Japan Acad. 46, 837-840 (1970; Zbl 0225.16010)] has shown that a left noetherian left QF-3 ring is also right QF-3. The present author generalizes this and shows that when R is left and right noetherian, then \(dom.\dim (R_ R)\geq 1\) if and only if \(dom.\dim (_ RR)\geq 1\).
scientific article; zbMATH DE number 4148334