Several authors have been interested in some like phantom morphisms such as $ d $-
phantoms, $ d $-$\operatorname {Ext} $-phantoms, neat-phantom morphisms, clean …

Let ℱ 𝒫∞ R be the class of all left R-modules M which has a projective resolution by finitely
generated projectives. An exact sequence 0→ A→ B→ C→ 0 of right R-modules is called …

A morphism f: M→ N of left R-modules is called an n-phantom morphism if the induced
morphism Tor n R (A, f)= 0 for every (finitely presented) right R-module A. Analogously, a …

A morphism f of left R-modules is called an RD-phantom morphism if the induced morphism
Tor1 (R= aR, f)= 0 for any a R. Similarly, a morphism g of left R-modules is said to be an …

A morphism f: M→ N f:M→N of left R-modules is called an n-phantom morphism (resp. a Tor
n-epimorphism) if the induced morphism Tor n (A, f)= 0 (resp. Tor n (A, f) is an epimorphism) …

In this paper, we first define the notion of finitely-cosmall quotient (singly-cosmall quotient)
morphisms. Then we give a characterization of this new concept. We show that an …

A morphism f: M→ N of left R-modules is called a phantom morphism if the induced
morphism for every (finitely presented) right R-module A. Similarly, a morphism g: M→ N of …

It is our intention in this research generalized some concept in local cohomology such as
contravarint functor $ ext $, covariant functor $ Ext $, covarian functor $ Tor $ and ideal …

In the case where $\mathbf {k}=\mathbb {F} _2 $, for $ S $ a contravariant functor from the
category of finite dimensional $\mathbf {k} $-vector spaces to the category of sets, and for …

Let $ R $ be a ring. A morphism $\alpha: X\rightarrow Y $ of left $ R $-modules is called a
finitely phantom morphism if for each morphism ${\beta: F\rightarrow X} $ with $ F $ finitely …