An application of a theorem of Ziegler
type: Item
instance of: scholarly article
title: An application of a theorem of Ziegler
zbMATH Open document ID: 0712.16015
DOI: 10.1007/BF01320697
author: Maher Zayed
published in: Monatshefte für Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178480
review text: The aim of this note is to prove that an Artin algebra (resp. a finite- dimensional algebra over an algebraically closed field) all of whose algebraically compact (resp. \(\Sigma\)-algebraically compact) indecomposable modules are finitely generated must be of finite- representation type. The result is derived with the aid of a theorem of Ziegler.
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16B70
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16P20
zbMATH DE Number: 4171153
zbMATH Keywords: algebraically compact module
zbMATH Keywords: ultraproduct
zbMATH Keywords: elementary equivalence
zbMATH Keywords: Artin algebra
zbMATH Keywords: finite-dimensional algebra
zbMATH Keywords: indecomposable modules
zbMATH Keywords: finite- representation type
MaRDI profile type: Publication
cites work: Q4056148
cites work: Representation Theory of Artin Algebras II
cites work: Q3884264
cites work: Rings of finite representation type and modules of finite Morley rank
cites work: Q3866236
cites work: Q4079762
cites work: Q5600865
cites work: Model theory of modules
OpenAlex ID: W2068851911
description: scientific article; zbMATH DE number 4171153