A morphism f: M→ N of left R-modules is called a phantom morphism if the induced
morphism for every (finitely presented) right R-module A. Similarly, a morphism g: M→ N of
left R-modules is said to be an Ext-phantom morphism if the induced morphism for every
finitely presented left R-module B. We prove that every left R-module has a phantom
preenvelope if R is a right coherent ring and every left R-module has an Ext-phantom cover
if R is a left coherent ring. In addition, we investigate the properties of precovers and …