Flat Covers and Flat Representations of Quivers

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.