Flat Covers and Flat Representations of Quivers

Abstract

Abstract This paper is devoted to the study of flat module representations. We characterize such representations for quivers not containing the path ·• → • (the so called rooted quivers). Then, we prove that for every such quiver any representation has a flat cover and a cotorsion envelope. We finally observe that if Q is one of those quivers and if ℱ denotes the class of all flat representations of Q, then the pair (ℱ, ℱ⊥) is a cotorsion theory.