On dominant dimension of Noetherian rings
type: Item
instance of: scholarly article
title: On dominant dimension of Noetherian rings
zbMATH Open document ID: 0701.16008
author: Mitsuo Hoshino
published in: Osaka Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: 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 \(dom.\dim (_ RR)\geq 1\).
reviewed by: Günter Krause
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16L60
zbMATH DE Number: 4148334
zbMATH Keywords: dual module
zbMATH Keywords: cogenerator
zbMATH Keywords: flat module
zbMATH Keywords: minimal injective resolution
zbMATH Keywords: dominant dimension
zbMATH Keywords: right QF-3
zbMATH Keywords: left noetherian left QF-3 ring
MaRDI profile type: Publication
Recommended article: On the Krull dimension of noetherian rings
Recommended article: An integral theory of dominant dimension of Noetherian algebras
Recommended article: Q2702064
Recommended article: Q5469466
Recommended article: Finitistic dimensions of Noetherian rings
Recommended article: On a conjecture about dominant dimensions of algebras
Recommended article: Q5690125
Recommended article: On reducing homological dimensions over Noetherian rings
Recommended article: On co-Noetherian dimension of rings.
Recommended article: Dominant dimension of semi-primary rings.
description: scientific article; zbMATH DE number 4148334