A Note on DG-Gorenstein Injective Complexes

2020 ◽  
Vol 27 (04) ◽  
pp. 731-740
Author(s):  
Bo Lu ◽  
Kaiyang Lan
Keyword(s):  
Gorenstein Injective

The notion of DG-Gorenstein injective complexes is studied in this article. It is shown that a complex G is DG-Gorenstein injective if and only if G is exact with [Formula: see text] Gorenstein injective in R-Mod for each [Formula: see text] and any morphism [Formula: see text] is null homotopic whenever E is a DG-injective complex.

New model structures and projective (injective) cotorsion pairs

2021 ◽  
Author(s):  
Aimin Xu
Keyword(s):  
Positive Integer ◽  
Triangulated Categories ◽  
Model Structure ◽  
Cotorsion Pair ◽  
Flat Dimension ◽  
Gorenstein Projective Module ◽  
Chain Complexes ◽  
Cotorsion Pairs ◽  
Gorenstein Injective ◽  
Model Structures

Let [Formula: see text] be either the category of [Formula: see text]-modules or the category of chain complexes of [Formula: see text]-modules and [Formula: see text] a cofibrantly generated hereditary abelian model structure on [Formula: see text]. First, we get a new cofibrantly generated model structure on [Formula: see text] related to [Formula: see text] for any positive integer [Formula: see text], and hence, one can get new algebraic triangulated categories. Second, it is shown that any [Formula: see text]-strongly Gorenstein projective module gives rise to a projective cotorsion pair cogenerated by a set. Finally, let [Formula: see text] be an [Formula: see text]-module with finite flat dimension and [Formula: see text] a positive integer, if [Formula: see text] is an exact sequence of [Formula: see text]-modules with every [Formula: see text] Gorenstein injective, then [Formula: see text] is injective.

Strict Mittag–Leffler modules over Gorenstein injective modules

2019 ◽  
Vol 19 (03) ◽  
pp. 2050050 ◽  
Author(s):  
Yanjiong Yang ◽  
Xiaoguang Yan
Keyword(s):  
Noetherian Ring ◽  
Direct Limit ◽  
Injective Module ◽  
Noetherian Rings ◽  
Projective Modules ◽  
Injective Modules ◽  
Pure Submodules ◽  
Covering Class ◽  
Gorenstein Injective ◽  
Finitely Presented

In this paper, we study the conditions under which a module is a strict Mittag–Leffler module over the class [Formula: see text] of Gorenstein injective modules. To this aim, we introduce the notion of [Formula: see text]-projective modules and prove that over noetherian rings, if a module can be expressed as the direct limit of finitely presented [Formula: see text]-projective modules, then it is a strict Mittag–Leffler module over [Formula: see text]. As applications, we prove that if [Formula: see text] is a two-sided noetherian ring, then [Formula: see text] is a covering class closed under pure submodules if and only if every injective module is strict Mittag–Leffler over [Formula: see text].

Gorenstein injective and projective complexes

1998 ◽  
Vol 26 (5) ◽  
pp. 1657-1674 ◽  
Author(s):  
Edgar E. Enochs ◽  
J.R. Garcí Rozas
Keyword(s):  
Gorenstein Injective

On gorenstein injective modules

1993 ◽  
Vol 21 (10) ◽  
pp. 3489-3501 ◽  
Author(s):  
Edgar E. Enochs ◽  
Overtoun M.G. Jenda
Keyword(s):  
Injective Modules ◽  
Gorenstein Injective

Gorenstein Injective and Gorenstein Flat Dimensions Under Base Change

2003 ◽  
Vol 31 (2) ◽  
pp. 991-1005 ◽  
Author(s):  
Leila Khatami ◽  
Siamak Yassemi
Keyword(s):  
Base Change ◽  
Gorenstein Flat ◽  
Gorenstein Injective

scholarly journals Relative Gorenstein injective covers with respect to a semidualizing module

2017 ◽  
Vol 67 (1) ◽  
pp. 87-95
Author(s):  
Elham Tavasoli ◽  
Maryam Salimi
Keyword(s):  
Semidualizing Module ◽  
Gorenstein Injective

WEAK AB-CONTEXT FOR FP-INJECTIVE MODULES WITH RESPECT TO SEMIDUALIZING MODULES

2013 ◽  
Vol 12 (07) ◽  
pp. 1350039 ◽  
Author(s):  
JIANGSHENG HU ◽  
DONGDONG ZHANG
Keyword(s):  
Noetherian Ring ◽  
Model Structure ◽  
Injective Dimension ◽  
Commutative Noetherian Ring ◽  
New Model ◽  
Injective Modules ◽  
Semidualizing Modules ◽  
Semidualizing Bimodule ◽  
Gorenstein Injective

Let S and R be rings and SCR a semidualizing bimodule. We define and study GC-FP-injective R-modules, and these modules are exactly C-Gorenstein injective R-modules defined by Holm and Jørgensen provided that S = R is a commutative Noetherian ring. We mainly prove that the category of GC-FP-injective R-modules is a part of a weak AB-context, which is dual of weak AB-context in the terminology of Hashimoto. In particular, this allows us to deduce the existence of certain Auslander–Buchweitz approximations for R-modules with finite GC-FP-injective dimension. As an application, a new model structure in Mod R is given.

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