On self-injective dimensions of Artinian rings
type: Item
instance of: scholarly article
title: On self-injective dimensions of Artinian rings
zbMATH Open document ID: 0823.16006
author: Mitsuo Hoshino
published in: Tsukuba Journal of Mathematics
publication date: 1994-12-19T00:00:00Z
review text: Let \(R\) be a left and right artinian ring and \(\text{mod }R\) the category of finitely generated left \(R\)-modules. The author studies the question when \(\text{inj dim }R_ R < \infty\) implies \(\text{inj dim }_ RR < \infty\). His main result is the following: Let \(m, n \geq 1\). Suppose that \(\text{inj dim }R_ R \leq n\) and that for all \(0 \leq i \leq n - 2\) \(\text{Ext}^ i_ R (\text{Ext}^ m_ R (-,R), R)\) vanishes on \(\text{mod }R\). Then \(\text{inj dim }_ RR < \infty\).
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16P20
zbMATH DE Number: 701543
zbMATH Keywords: injective dimension
zbMATH Keywords: projective dimension
zbMATH Keywords: right Artinian rings
zbMATH Keywords: category of finitely generated left modules
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496162450
OpenAlex ID: W216081190
Wikidata QID: Q114047166
DOI: 10.21099/TKBJM/1496162450
description: scientific article; zbMATH DE number 701543