A note on Fuller's theorem
type: Item
instance of: scholarly article
title: A note on Fuller's theorem
zbMATH Open document ID: 0689.16020
author: Shenglin Zhu
published in: Chinese Annals of Mathematics. Series B
publication date: 1989-01-01T00:00:00Z
review text: Let R, \(\Delta\) be rings, \({}_ RC\) a complete additive subcategory of R-Mod, T: \(\Delta\)-Mod\(\to_ RC\) a category equivalence, \({}_ RU=T(\Delta)\). If \({}_ RU\) is projective then \({}_ RC\) is closed under extensions and for simple left R-modules S, \(S'\) it is \(S'\in_ RC\) provided \(S\in_ RC\) and \(Ext^ 1_ R(S,S')\neq 0\). The converse holds if R is right perfect and each simple module in \({}_ RC\) is finitely presented (Th.2). If R is left Artinian and \({}_ RC\) is category equivalent to R-Mod, then \({}_ RC=R\)-Mod (Th.5).
reviewed by: Ladislav Bican
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16L30
Mathematics Subject Classification ID: 18E05
zbMATH DE Number: 4129020
zbMATH Keywords: right perfect ring
zbMATH Keywords: left Artinian ring
zbMATH Keywords: complete additive subcategory
zbMATH Keywords: category equivalence
zbMATH Keywords: extensions
zbMATH Keywords: simple left R-modules
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4129020