International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 70, Pages 4409-4419
doi:10.1155/S0161171203205391

Flat covers of representations of the quiver A∞

E. Enochs,1 S. Estrada,2 J. R. García Rozas,2 and L. Oyonarte2

1Department of Mathematics, University of Kentucky, Lexington 40506-0027, KY, USA
2Departamento de Álgebra y Análisis Matemático, Universidad de Almería, Almería 04071, Spain

Received 21 May 2002

Copyright © 2003 E. Enochs et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Rooted quivers are quivers that do not contain A∞≡⋯→•→• as a subquiver. The existence of flat covers and cotorsion envelopes for representations of these quivers have been studied by Enochs et al. The main goal of this paper is to prove that flat covers and cotorsion envelopes exist for representations of A∞. We first characterize finitely generated projective representations of A∞. We also see that there are no projective covers for representations of A∞, which adds more interest to the problem of the existence of flat covers.