… T has the universal property with respect to these conditions. The … We call such a morphism
f, as an n-Ext-phantom morphism. In … The aim of this section is to study a subfunctor of Extn …

… On the other hand, Gorenstein homological algebra is a relative version of homological …
Ext . In the following proposition, we show that over commutative coherent rings two subfunctors …

… In [5], Fu, Guil Asensio, Herzog and Torrecillas introduced a relative version of phantom
morphisms in the sense: For an additive subfunctor F of Ext, a morphism ϕ : X → A in R-Mod is …

… In 2018, Mao introduced the concept of n-phantom morphism [14], which is a higher … different
characterizations with regard to the weak dimensions of a ring R by n-phantom envelope (n-…

… may be viewed as the morphism versions of flat and absolutely pure modules. We have known
that phantom and cophantom morphisms admit … Recall that an additive subfunctor F of Ext …

… corresponds to an additive subfunctor of Ext. It has been … [22], which extended the theory of
approximation in the relative … such as the Auslander–Reiten phantom morphisms. [22] work in …

… of ideals is the ideal of phantom morphisms. The study of phantom morphisms has its
roots in … Now we consider the cokernel of a phantom envelope and the kernel of an \(\mathrm{Ext}\)-…

… phenomena’ into the exact category setting by means of additive subfunctors F of Ext in ( A ,
… yields the corresponding notion of ideal of relative phantom maps (denoted by Φ ( E s t ) and …

… the notions of Fn-phantoms and Fncophantoms (relative to En). … , I(−,−) is a subfunctor
of the Hom-bifunctor A(−,−). … for phantom A-ideals in the following way: if E is a phantom A-ideal …

… of n-phantom morphisms and n-Ext-phantom morphisms. Journal of … the n-phantom and
n-Ext-phantom of morphisms in short … ) and their character morphisms has been investigated. …