… We first consider the phantom precovers and preenvelopes under change of rings. …
Next we study the Ext-phantom precovers and preenvelopes under change of rings. …

… Ext-phantom morphisms are also called cophantom morphisms in [14]. On the other hand,
the concepts of precovers and preenvelopes … module has an Ext-phantom preenvelope (which …

… to be an RD-Ext-phantom morphism if the induced morphism … a morphism is an RD-Ext-phantom
morphism if and only if the … , Precovers and preenvelopes by phantom and Ext-phantom …

… right module A and α is said to be an n-Ext-phantom if Extn(A, α) is 0 for every finitely … ., a
1-Ext-phantom) morphism if and only if α is a phantom (resp., an Ext-phantom) morphism. On …

… is an Ext-phantom morphism. We also investigate the existence of precovers and preenvelopes
by n-phantom and n-Ext-phantom morphisms. For instance, we prove that every left R-…

… Similarly, a morphism g : X → Y of left R-modules is called a cophantom morphism or Ext-phantom
morphism [15, 22] if the induced morphism Ext …

… We prove that every left R-module M has an Ext-phantom preenvelope f: M → N with coker(f)
… Ext-phantom α: M → N in R-Mod is an Ext-phantom preenvelope of M if for any Ext-phantom …

… Using some special morphisms of modules such as phantom, Ext -phantom, flat and
absolutely pure morphisms, we give some new characterizations of left coherent rings, von …

… and the collection of n-Ext-phantom morphisms in R-Mod are … and the ideal of n-Ext-phantom
morphisms by n. The category … : Precovers and preenvelopes by phantom and Ext-phantom …

… The concepts of precovers and preenvelopes (approximations) were introduced in the early
… left R-modules is said to be a cophantom morphism or Ext-phantom morphism [8, 13] if the …