It is possible to associate a topological space to the category of modules over any ring. This
space, the Ziegler spectrum, is based on the indecomposable pure-injective modules …

Let (A; E) be an exact category and F⊆ Ext a subfunctor. A morphism φ in A is an F-phantom
if the pullback of an E-conflation along φ is a conflation in F. If the exact category (A; E) has …

The mono-epi (ME) exact structure on the morphisms of an exact category is introduced and
used to prove ideal versions of Salce's Lemma, Christensen's (Ghost) Lemma, and …

In this paper, we introduce and study relative phantom morphisms in extriangulated
categories defined by Nakaoka and Palu. Then using their properties, we show that if (𝒞, 𝔼 …

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 …

We study the existence of covers and envelopes by some special functors on the category of
finitely presented modules. As an application, we characterize some important rings using …

Covering ideals of morphisms and module representations of the quiver A2 - ScienceDirect
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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 …

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) …

We develop a general theory of partial morphisms in additive exact categories which
extends the model theoretic notion introduced by Ziegler in the particular case of pure-exact …