… an n-Ext-phantom morphism if the induced morphism Extn … properties of n-phantom and
n-Ext-phantom morphisms. Some … of n-phantom and n-Ext-phantom morphisms, which are …

… based on phantom envelopes and Ext-phantom covers of … replacing phantom and Ext-phantom
with n-phantom and n-… of n-phantom morphism [14], which is a higher dimensional …

… It is proven that a morphism f is an n-phantom morphism if and … ; A morphism g is an n-Ext-phantom
morphism if and only if … n-phantom morphisms by n and the ideal of n-Ext-phantom …

… morphism if the induced morphism Ext1(R/Ra, ) = 0 for any a ∈ R. It is proven that a morphism
f is an RD-phantom morphism … ; a morphism is an RD-Ext-phantom morphism if and only if …

… Ext-phantom morphisms are also called cophantom morphisms in [14]. … We note that the
existence of Ext-phantom preenvelopes is a special case of [14, Theorems 32 and 33]. In Sect. 2 …

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

… cophantom morphism or Ext-phantom morphism [15, 22] if the induced … morphism versions
of flat and absolutely pure modules. We have known that phantom and cophantom morphisms …

… [14] that is, in some respects, better behaved. A significant portion of relative homological …
also refer to a P-Ext-phantom as a pure phantom morphism. The complete ideal cotorsion …

… We call such a morphism f, as an n-Ext-phantom morphism. In Section 7, we introduce a
composition operator “◦” on Extn /P. It is shown that this operator is associative and distributive …

… For example, if C is the class of finitely presented right R-modules, then C ⊤ is just the ideal
of phantom morphisms of R-Mod in [11] and C ⊥ is just the ideal of Ext-phantom morphisms …