In this paper, Gorenstein FP-injective modules are introduced and studied. An R-module M
is called Gorenstein FP-injective if there is an exact sequence⋯→ E1→ E0→ E0→ E1→⋯ of …

We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …

Let R be a ring. A left R-module M (respectively right R-module N) is called FI-injective
(respectively FI-flat) if Ext1 (G, M)= 0 (respectively Tor1 (N, G)= 0) for any FP-injective left R …

We study two notions of purity in categories of sheaves: the categorical and the geometric. It
is shown that pure injective envelopes exist in both cases under very general assumptions …

In this article, Gorenstein FP-injective modules are introduced and investigated. A left R-
module M is called Gorenstein FP-injective if there is an exact sequence…→ E 1→ E 0→ E …

Let R be a ring. Recall that a left R-module M is coherent if every finitely generated
submodule of M is finitely presented. R is a left coherent ring if the left R-module RR is …

We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …

In this paper we extend the notion of FP-injective modules to that of complexes and
characterize such complexes. We show that some characterizations similar to those for …

We establish equivalent conditions under which every object in an Abelian category has a
monic X-cover and an epic X-envelope respectively, when X is a class of objects closed …

Recently, many authors have embraced the study of certain properties of modules such as
projectivity, injectivity and flatness from an alternative point of view. This way, Durgun has …