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 …

The coherent sheaves defined on a separated noetherian scheme X reflect the underlying
geometry, and they play a central role in modern algebraic geometry. Recent results have …

Let R be a ring, na fixed non-negative integer and ℱ ℐ n (ℱ n) the class of all right (left) R-
modules of FP-injective (flat) dimension at most n. We prove that (is a perfect cotorsion …

We define a dimension, called an FP-projective dimension, for modules and rings. It
measures how far away a finitely generated module is from being finitely presented, and …

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 …

A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A
left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext1 (G, M)= 0 …

Let R be a ring. A right R-module C is called cotorsion if for any flat right R-module biF. In
this paper, we first give some results on cotorsion envelopes that are analogous to those on …

A ring R is called “left generalized morphic” if for every element a in R, there exists b∈ R
such that l (a)≅ R/Rb, where l (a) denotes the left annihilator of a in R. The aim of this article …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …

Let $ R $ be a commutative ring, and let $ S $ be a multiplicative subset of $ R $. In this
paper, we investigate the notion of $ S $-cotorsion modules. An $ R $-module $ C $ is called …