… has a phantom cover and an Ext-phantom preenvelope in R-… of phantom preenvelopes and
Ext-phantom precovers in R-Mod… bijective correspondence between an ℐ-preenvelope (resp. …

… of precovers and preenvelopes (… an Ext-phantom preenvelope (which is a monomorphism)
with the cokernel pure-projective. We note that the existence of Ext-phantom preenvelopes is …

… We know that the concepts of preenvelopes and precovers (approximations) were introduced …
We note that the existence of Ext-phantom preenvelopes is a special case of the works [6, …

… Just as a phantom precover is called special [22, p. 230] … RD-phantom precover f : M → N
special if the kernel of f is RD-injective. Similarly, we will call an RD-Ext-phantom preenvelope : …

… 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-…

… ] when its kernel is cotorsion, we will call a phantom precover c:M → N special if the kernel
of c is pure injective. Given a module N, a special phantom precover may be easily produced. …

… phantom morphisms such as d-phantoms, d-Ext-phantoms, … Dually, we have the definitions
of a C-preenvelope and a C-… An I-precover is called I-cover if every endomorphism h of M …

… ; A morphism g is an n-Ext-phantom morphism if and only if the … has an object-special n-phantom
precover. In addition, we … Dually we have the definitions of a c-preenvelope and a c…

… We prove that every left R-module M has an Ext-phantom preenvelope f: M → N with coker(f)
… Recall from [Citation20] that a phantom φ: B → A in R-Mod is a phantom precover of A if for …

… for the study of precovers and preenvelopes (approximation … between special precovering
ideals and phantom morphisms … phantoms are defined relative to the subfunctor Pext of Ext R …