Bouquets of Baer modules
type: Item
instance of: scholarly article
title: Bouquets of Baer modules
zbMATH Open document ID: 0817.16006
DOI: 10.1016/0022-4049(94)90092-2
author: Frank Okoh
published in: Journal of Pure and Applied Algebra
publication date: 1995-07-31T00:00:00Z
review text: In the category \(R\)-mod over a path \(K\)-algebra over extended Coxeter- Dynkin diagrams with no oriented cycles a torsion theory is introduced in the natural way. A torsion-free \(R\)-module \(M\) of countable rank is Baer (\(\text{Ext}(T,M) = 0\) for each \(T\) torsion) if and only if every finite rank submodule is finite-dimensional if and only if \(M = \bigcup_{n = 1}^ \infty M_ n\), where \(M_ n \subset M_{n+1}\), \(n = 1, \ldots,\) are finite dimensional submodules of \(M\) with \(M/M_ n\) torsion-free (Th. 1.2). The second part investigates systems \(\mathcal B = \{B_ n\}_{n = 0}^ \infty\) of Baer modules which are rigid in the following sense: The automorphism group of \(B_ n\) is the multiplicative group of \(K\), \(B_ n\) and \(B_ m\) are not isomorphic whenever \(m \neq n\) and \(\text{Ext}(B_ m, B_ n) = 0\) for every pair of positive integers \(m\), \(n\) (Th. 2.4). In the last paragraph the \(\aleph_ r\)-Baer modules (every submodule of \(M\) of cardinality less than \(\aleph_ r\) is Baer) are treated. Among other results the existence of an \(\aleph_ 1\)-Baer but not Baer module is proved.
reviewed by: Ladislav Bican
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16S90
zbMATH DE Number: 584668
zbMATH Keywords: path algebras
zbMATH Keywords: extended Coxeter-Dynkin diagrams
zbMATH Keywords: torsion theory
zbMATH Keywords: finite rank submodule
zbMATH Keywords: finite dimensional submodules
zbMATH Keywords: Baer modules
zbMATH Keywords: automorphism group
zbMATH Keywords: multiplicative group
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90092-2
OpenAlex ID: W2028377238
cites work: A note on wild quiver algebras and tilting modules
cites work: Indecomposable representations of graphs and algebras
cites work: Baer modules over valuation domains
cites work: Baer Modules over Domains
cites work: On Algebraic Equivalence Between Pairs of Linear Transformations
cites work: Q5609457
cites work: Q4729884
cites work: Perpendicular categories with applications to representations and sheaves
cites work: New aspects for two classical theorems on torsion splitting*
cites work: A Solution to the Splitting Mixed Group Problem of Baer
cites work: Q3999266
cites work: Q4059077
cites work: Q3310781
cites work: A class of infinite-rank modules over tame hereditary algebras
cites work: Baer modules.
cites work: Indecomposable modules constructed from Liouville numbers
cites work: Q3789728
cites work: Separable modules over finite-dimensional algebras
cites work: Pure-injective modules over path algebras
cites work: Q3866236
description: scientific article; zbMATH DE number 584668