… existence of Ext-phantom preenvelopes is a special case of [14… monomorphism is a phantom
envelope of a left R-module, then … {Ext}\)-phantom cover of a left R-module, then its kernel is …

… module has a phantom preenvelope if R is a right coherent ring and every left R-module has
an Ext-phantom cover … the existence of (pre)covers and (pre)envelopes with respect to some …

… conclusions based on phantom envelopes and Ext-phantom covers of modules, and we find
… after replacing phantom and Ext-phantom with n-phantom and n-Ext-phantom respectively. …

… left R-module has an n-Ext-phantom cover and n-Ext-phantom … terms of envelopes and covers
by n-phantom and n-Ext-phantom … with identity and all modules are unitary. The character …

… module has an epic RD-phantom cover with the kernel RD-injective and has a monic RD-Ext-phantom …
In ideal approximation theory, the concepts of classical covers and envelopes for …

… modules in terms of, among others, torsion theories. We also describe the relationship
between phantoms and Ext-phantoms … We prove that every left R-module M has an Ext-phantom …

… phantom if Torn(A, α) = 0 for any finitely presented right module A and α is said to be an n-Ext-phantom …
This theory is a generalization of the classical theory of covers and envelopes (…

… R-modules is called a cophantom morphism or Ext-phantom … ring R, every R-module has a
neatphantom cover with a neat-… of neat-injective envelope of a module, we need the following …

… -phantom morphisms by n and the ideal of n-Ext-phantom morphisms by n. The category of
morphisms of modules … We first recall the definitions of (pre)covers and (pre)envelopes. Let A …

… In this case, a morphism f: X→ A is a phantom morphism if … injective module may be taken to
be the injective envelope of … to a P-Ext-phantom as a pure phantom morphism. The complete …