For any ring R we construct two triangulated categories, each admitting a functor from R-
modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or …

The main objective of this paper is to study the relative derived categories from various
points of view. Let A be an abelian category and C be a contravariantly finite subcategory of …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact …

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 introduce the notion of G-liftable ideals, which extends the liftable ideas
defined by Assem and Le Meur. We characterize the G-liftable ideals and construct the …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …

Acta Mathematica Sinica, English Series Page 1 Acta Mathematica Sinica, English Series
Nov., 2017, Vol. 33, No. 11, pp. 1513–1535 Published online: July 15, 2017 https://doi.org/10.1007/s10114-017-6416-8 …

In this paper we study the finiteness of global Gorenstein AC-homological dimensions for
rings, and answer the questions posed by Becerril, Mendoza, Pérez and Santiago. As an …

Let R be a ring with identity and C (R) denote the category of complexes of R-modules. In
this paper we study the homotopy categories arising from projective (resp. injective) …

In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an
R-module M, we show that M is Gorenstein injective if and only if Hom R (Ȓ, M) belongs to …