Precovers and Preenvelopes by Phantom and Ext-Phantom Morphisms.

A morphismf:M → Nof leftR-modules is called a phantom morphism if the induced morphismfor every (finitely presented) rightR-moduleA. Similarly, a morphismg:M → Nof leftR-modules is said to be an Ext-phantom morphism if the induced morphismfor every finitely presented leftR-moduleB. We prove that every leftR-module has a phantom preenvelope ifRis a right coherent ring and every leftR-module has an Ext-phantom cover ifRis a left coherent ring. In addition, we investigate the properties of precovers and preenvelopes by phantom and Ext-phantom morphisms under change of rings. [ABSTRACT FROM PUBLISHER]