Flat covers of representations of the quiver \(A_\infty\).
type: Item
instance of: scholarly article
title: Flat covers of representations of the quiver \(A_\infty\).
zbMATH Open document ID: 1066.16011
DOI: 10.1155/S0161171203205391
author: J. R. García Rozas
author: E. Enochs
author: S. Estrada
author: Luis Oyonarte
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-09T00:00:00Z
full work available at URL: https://eudml.org/doc/51434
review text: Summary: Rooted quivers are quivers that do not contain \(A_\infty\equiv\cdots\to\bullet\to\bullet\) as a subquiver. The existence of flat covers and cotorsion envelopes for representations of these quivers have been studied by \textit{E. Enochs, L. Oyonarte} and \textit{B. Torrecillas} [Commun. Algebra 32, No. 4, 1319-1338 (2004; Zbl 1063.16017)]. The main goal of this paper is to prove that flat covers and cotorsion envelopes exist for representations of \(A_\infty\). We first characterize finitely generated projective representations of \(A_\infty\). We also see that there are no projective covers for representations of \(A_\infty\), which adds more interest to the problem of the existence of flat covers.
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16D40
zbMATH DE Number: 2166342
zbMATH Keywords: rooted quivers
zbMATH Keywords: flat covers
zbMATH Keywords: cotorsion envelopes
zbMATH Keywords: representations of quivers
zbMATH Keywords: finitely generated projective representations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2166342