Flat covers of representations of the quiver \(A_\infty\). (English) Zbl 1066.16011

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 E. Enochs, L. Oyonarte and 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.


16G20 Representations of quivers and partially ordered sets
16D40 Free, projective, and flat modules and ideals in associative algebras


Zbl 1063.16017
Full Text: DOI EuDML