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: 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) …

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 …

This paper extends many conclusions based on phantom envelopes and Ext-phantom
covers of modules, and we find that many important properties still hold after replacing …

Suppose (R, m) and (S, n) are commutative Noetherian local rings and ϕ: R→ S is a flat
local homomorphism with the property that the induced homomorphism R/m→ S/mS is …

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A ring extension is a ring homomorphism preserving identities. In this paper, we give the
definition of relatively free modules on ring extensions and develop some basic properties of …

Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism
Y→ M is neat in Y, ie, the induced map Hom (S, Y)→ Hom (S, M) is surjective for any simple …

It is proved that if R is a right FBN ring then a non-zero right R-module M has the property
that HomR (M, N)≠ 0 for every non-zero submodule N of M if and only if HomR (M, R/P)≠ 0 …

In this paper, we introduce a general form of pseudo-p-injectivity. Let be a right-module
and=(), its endomorphism ring. A right-module is called a generalized-pseudo-Mp-injective …